Etymology
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firm (adj.)

late 14c., ferm, "strong, steady" (of things), "permanent, enduring" (of agreements), "steadfast, steady" (of persons), "sound, well-founded" (of arguments), from Old French ferm "strong, vigorous; healthy, sound; steadfast, loyal, faithful" (12c.), from Latin firmus "strong, steadfast, enduring, stable," figuratively "constant, steadfast, trusty, faithful," from suffixed form of PIE root *dher- "to hold firmly, support." The spelling return to -i- in late 1500s was modeled on Latin. Related: Firmly; firmness.

firm (n.)

"business house," 1744, according to Barnhart from German Firma "a business, name of a business," originally "signature," from Italian firma "signature," from firmare "to sign," from Latin firmare "make firm, affirm," in Late Latin, "confirm (by signature)," from firmus "strong; stable," figuratively "constant, trusty" (see firm (adj.)).

firm (v.)

c. 1300, fermen "make firm, establish," from Old French fermer "consolidate; fasten, secure; build, set up; fortify" (12c.) or directly from Latin firmare "make firm; affirm; strengthen, fortify, sustain; establish, prove, declare," from firmus "strong, steadfast, stable" (see firm (adj.)). Intransitive use, "become firm" is from 1879; with up (adv.) from 1956. Related: Firmed; firming.

updated on January 28, 2018

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Definitions of firm from WordNet
1
firm (adj.)
unwavering in devotion to friend or vow or cause; "the true-hearted soldier...of Tippecanoe"- Campaign song for William Henry Harrison;
a firm ally
Synonyms: loyal / truehearted / fast
firm (adj.)
marked by firm determination or resolution; not shakable;
a firm mouth
firm convictions
Synonyms: steadfast / steady / stiff / unbendable / unfaltering / unshakable / unwavering
firm (adj.)
not soft or yielding to pressure;
the snow was firm underfoot
a firm mattress
Synonyms: solid
firm (adj.)
strong and sure;
a firm grasp
Synonyms: strong
firm (adj.)
not subject to revision or change;
a firm contract
a firm offer
firm (adj.)
(of especially a person's physical features) not shaking or trembling;
a firm step
his voice was firm and confident
firm (adj.)
not liable to fluctuate or especially to fall;
stocks are still firm
Synonyms: steady / unfluctuating
firm (adj.)
securely established;
holds a firm position as the country's leading poet
firm (adj.)
possessing the tone and resiliency of healthy tissue;
firm muscles
firm (adj.)
securely fixed in place;
the post was still firm after being hit by the car
Synonyms: fast / immobile
2
firm (v.)
become taut or tauter;
Your muscles will firm when you exercise regularly
Synonyms: tauten
firm (v.)
make taut or tauter;
Synonyms: tauten
3
firm (n.)
the members of a business organization that owns or operates one or more establishments;
Synonyms: house / business firm
4
firm (adv.)
with resolute determination;
you must stand firm
Synonyms: firmly / steadfastly / unwaveringly
Etymologies are not definitions. From wordnet.princeton.edu, not affiliated with etymonline.