underpin (v.) Look up underpin at Dictionary.com
"support or prop," 1520s (figurative); 1530s (literal), from under + pin (v.). Related: Underpinned; underpinning.
underpinning (n.) Look up underpinning at Dictionary.com
late 15c., "action of supporting or strengthening from beneath," from under + present participle of pin (v.). Figurative sense of "prop, support" is recorded from 1580s.
underprivileged (adj.) Look up underprivileged at Dictionary.com
1896, from under + past participle of privilege (v.). Noun use (short for underprivileged persons) is attested from 1935.
underrate (v.) Look up underrate at Dictionary.com
also under-rate, 1640s, "to esteem at too little worth," from under + rate (v.). Related: Underrated; underrating.
underscore (v.) Look up underscore at Dictionary.com
1771, "to draw a line under," from under + score (v.). The figurative sense of "to emphasize" is attested from 1891. Noun meaning "a line drawn below (something)" is recorded from 1901.
undersea (adj.) Look up undersea at Dictionary.com
1610s, from under + sea.
underserve (v.) Look up underserve at Dictionary.com
"to serve insufficiently," 1710, from under + serve (v.). Related: Underserved; underserving.
undershirt (n.) Look up undershirt at Dictionary.com
1640s, from under (adj.) + shirt (n.). Similar formation in North Frisian onnersjürt, Danish underskjorte. Old English had undersyrc (see sark (n.)).
undershoot (v.) Look up undershoot at Dictionary.com
1660s, "to shoot too low," from under + shoot (v.). In reference to aircraft or pilots, recorded from 1918. Undershot as a type of water wheel is recorded from c.1600.
underside (n.) Look up underside at Dictionary.com
1680s, from under (adj.) + side (n.). Similar formation in Dutch onderzijde, Danish underside, German unterseite.
undersign (v.) Look up undersign at Dictionary.com
1570s, from under + sign (v.). Related: Undersigned; undersigning.
understand (v.) Look up understand at Dictionary.com
Old English understandan "comprehend, grasp the idea of," probably literally "stand in the midst of," from under + standan "to stand" (see stand (v.)). If this is the meaning, the under is not the usual word meaning "beneath," but from Old English under, from PIE *nter- "between, among" (cognates: Sanskrit antar "among, between," Latin inter "between, among," Greek entera "intestines;" see inter-). Related: Understood; understanding

That is the suggestion in Barnhart, but other sources regard the "among, between, before, in the presence of" sense of Old English prefix and preposition under as other meanings of the same word. "Among" seems to be the sense in many Old English compounds that resemble understand, such as underniman "to receive," undersecan "examine, investigate, scrutinize" (literally "underseek"), underðencan "consider, change one's mind," underginnan "to begin." It also seems to be the sense still in expressions such as under such circumstances.

Perhaps the ultimate sense is "be close to;" compare Greek epistamai "I know how, I know," literally "I stand upon." Similar formations are found in Old Frisian (understonda), Middle Danish (understande), while other Germanic languages use compounds meaning "stand before" (German verstehen, represented in Old English by forstanden). For this concept, most Indo-European languages use figurative extensions of compounds that literally mean "put together," or "separate," or "take, grasp" (see comprehend). Old English oferstandan, Middle English overstonden, literally "over-stand" seem to have been used only in literal senses. For "to stand under" in a physical sense, Old English had undergestandan.
understandable (adj.) Look up understandable at Dictionary.com
late 14c., "able to understand;" late 15c., "able to be understood," from understand + -able. Related: Understandably.
understanding (n.) Look up understanding at Dictionary.com
Old English understanding "comprehension," verbal noun from understand (v.). Meaning "mutual agreement" is attested from 1803.
understate (v.) Look up understate at Dictionary.com
1781, from under + state (v.). Related: Understated; understating.
understated (adj.) Look up understated at Dictionary.com
1939, of clothing, fashions, writing, etc., figurative use of the past participle of understate (v.).
understatement (n.) Look up understatement at Dictionary.com
1799, from under + statement.
understory (n.) Look up understory at Dictionary.com
in reference to forest vegetation, also under-story, 1902, from under + story (n.).
understudy (v.) Look up understudy at Dictionary.com
also under-study, 1852, in the theatrical sense "memorize a part so as to be capable of performing on short notice it in the absence of the one to which it is assigned," from under + study (v.). The noun is attested from 1848, translating Italian supplimento.
undertake (v.) Look up undertake at Dictionary.com
c.1200, "to entrap;" c.1300, "to set about (to do)," from under + take (v.). Similar formation in French entreprendre "to undertake," from entre "between, among" + prendre "to take." The under in this word may be the same one that also may form the first element of understand. Old English had underniman "to trap, accept" (cognate with Dutch ondernemen, German unternehmen).
undertaker (n.) Look up undertaker at Dictionary.com
c.1400, "a contractor or projecter of any sort," agent noun from undertake (v.). The specialized sense (1690s) emerged from funeral-undertaker.
undertaking (n.) Look up undertaking at Dictionary.com
"enterprise," early 15c., verbal noun from undertake (v.). An Old English word for this was underfangenes.
undertone (n.) Look up undertone at Dictionary.com
1762, "low or subdued tone," from under + tone (n.). Figurative sense of "undercurrent of feelings, etc.," is attested from 1861.
undertow (n.) Look up undertow at Dictionary.com
1798, from under + tow (n.).
underutilize (v.) Look up underutilize at Dictionary.com
also under-utilize, 1949, from under + utilize. Related: Underutilized; underutilizing.
undervalue (v.) Look up undervalue at Dictionary.com
1590s, "to rate as inferior in value" (to), from under + value (v.). Sense of "to estimate or esteem too low" is recorded from 1610s. Meaning "to rate at too low a monetary value" is attested from 1620s. Related: Undervalued; undervaluing.
underwater (adj.) Look up underwater at Dictionary.com
1620s, from under + water (n.1). Of mortgages from 2008.
underway (adv.) Look up underway at Dictionary.com
1749, of ships, "having begun to move," from under + way (n.). In reference to projects, activities, etc., it is attested from 1935.
underwear (n.) Look up underwear at Dictionary.com
"undergarments," 1872, from under + wear (n.). So called because they are worn under one's clothing.
underweight (adj.) Look up underweight at Dictionary.com
1899, from under- + weight.
underwhelm (v.) Look up underwhelm at Dictionary.com
1953 (implied in underwhelming), a facetious play on overwhelm, with under. Related: Underwhelmed; underwhelmingly.
underworld (n.) Look up underworld at Dictionary.com
c.1600, "the lower world, Hades, place of departed souls," also "the earth, the world below the skies," as distinguished from heaven. Similar formation in German unterwelt, Dutch onderwereld, Danish underverden. Meaning "lower level of society" is first recorded 1890; "criminals and organized crime collectively" is attested from 1900.
underwrite (v.) Look up underwrite at Dictionary.com
Old English underwritan "write at the foot of; subscribe;" see under + write (v.). A loan-translation of Latin subscribere (see subscribe). Used literally at first; modern sense of "to accept the risk of insurance" (1620s) is from notion of signing a marine insurance policy. Meaning "to support by a guarantee of money" is recorded from 1890.
underwriter (n.) Look up underwriter at Dictionary.com
1610s, "subscriber," agent noun from underwrite (v.). Insurance sense is from 1620s.
undeserved (adj.) Look up undeserved at Dictionary.com
late 14c., from un- (1) "not" + past participle of deserve (v.). Related: Undeservedly.
undeserving (adj.) Look up undeserving at Dictionary.com
1540s, from un- (1) "not" + present participle of deserve (v.).
undesirable (adj.) Look up undesirable at Dictionary.com
1660s, "not to be desired, objectionable," from un- (1) "not" + desirable. The noun meaning "undesirable person or thing" is first attested 1883. Undesired "not asked or invited" is recorded from late 15c.
undetectable (adj.) Look up undetectable at Dictionary.com
1789, from un- (1) "not" + detectable (see detect (v.)).
undetected (adj.) Look up undetected at Dictionary.com
1590s, from un- (1) "not" + past participle of detect (v.).
undetermined (adj.) Look up undetermined at Dictionary.com
mid-15c., from un- (1) "not" + past participle of determine (v.).
undeterred (adj.) Look up undeterred at Dictionary.com
c.1600, from un- (1) "not" + past participle of deter (v.).
undeveloped (adj.) Look up undeveloped at Dictionary.com
1736, from un- (1) "not" + past participle of develop (v.). In reference to film, it is attested from 1939.
undeviating (adj.) Look up undeviating at Dictionary.com
1732, from un- (1) "not" + present participle of deviate.
undeviating (adj.) Look up undeviating at Dictionary.com
1732, from un- (1) "not" + present participle of deviate (v.).
undies (n.) Look up undies at Dictionary.com
1906, diminutive euphemistic abbreviation for women's underwear (or undergarments).
undifferentiated (adj.) Look up undifferentiated at Dictionary.com
1862, from un- (1) "not" + past participle of differentiate (v.).
undigested (adj.) Look up undigested at Dictionary.com
1520s, from un- (1) "not" + past participle of digest (v.). Figurative sense is recorded from c.1600.
undignified (adj.) Look up undignified at Dictionary.com
1680s, of clergy, "not holding a position of dignity," from un- (1) "not" + dignified. Meaning "lacking in dignity of manner" is attested from 1782.
undiluted (adj.) Look up undiluted at Dictionary.com
1756, from un- (1) "not" + past participle of dilute (v.).
undiminished (adj.) Look up undiminished at Dictionary.com
1580s, from un- (1) "not" + past participle of diminish (v.).