c. 1200, pointe, "minute amount, single item in a whole; sharp end of a sword, etc.," a merger of two words, both ultimately from Latin pungere "to prick, pierce," from a nasalized form of PIE root *peuk- "to prick."
The Latin neuter past participle punctum was used as a noun, meaning "small hole made by pricking," subsequently extended to anything that looked like one, hence, "dot, particle," etc. This yielded Old French point "dot; smallest amount," which was borrowed in Middle English in the "smallest amount" sense by c. 1300. The meaning "small mark, dot" (mark made by the end of a pointed instrument) in English is from mid-14c.
Meanwhile the Latin fem. past participle of pungere was puncta, which was used in Medieval Latin to mean "sharp tip," and became Old French pointe "point of a weapon, vanguard of an army," which also passed into English (early 14c.). The senses have merged in English, but remain distinct in French.
The sense of "peak or promontory from a land or coast" is from 1550s. The extended senses often are from the notion of "minute, single, or separate items in an extended whole." The sense of "brief period of time, instant" is from late 14c. Meaning "distinguishing feature" (especially a good one) is recorded from late 15c. Meaning "a unit of score in a game" is recorded from 1746.
The meaning "recognized unit of fluctuation of price per share on an exchange" is by 1814. As a typeface unit (in Britain and U.S., one twelfth of a pica), it went into use in U.S. 1883. As a measure of weight for precious stones (one one-hundredth of a carat) it is recorded from 1931. Meaning "diacritical mark indicating a vowel or other modification of sound" is from 1610s.
The point "the matter being discussed" is attested from late 14c.; meaning "sense, purpose, end, aim, advantage" (usually in the negative, as in what's the point?) is recorded by 1903. Point of honor (1610s) translates French point d'honneur. Point of no return (1941) is originally aviators' term for the point in a flight "before which any engine failure requires an immediate turn around and return to the point of departure, and beyond which such return is no longer practical" [Young America's Aviation Annual]. To make a point of "be resolved to do something and do it accordingly" is from 1778.
late 14c., "indicate with the finger;" c. 1400, "wound by stabbing; make pauses in reading a text; seal or fill openings or joints or between tiles," partly from Old French pointoier "to prick, stab, jab, mark," and also from point (n.).
From mid-15c. as "to stitch, mend." From late 15c. as "furnish (a garment) with tags or laces for fastening;" from late 15c. as "aim (something), direct toward an object." Related: Pointed; pointing. To point up "emphasize" is from 1934; to point out "indicate, show, make manifest" is from 1570s.