ball (n.2) Look up ball at Dictionary.com
"dancing party, social assembly for dancing," 1630s, from French, from Old French baller "to dance," from Late Latin ballare "to dance," from Greek ballizein "to dance, jump about" (see ballistics). Hence, "very enjoyable time," 1945, American English slang, perhaps back to 1930s in African-American vernacular.
ball (v.) Look up ball at Dictionary.com
1650s, "make into a ball," from ball (n.1). Intransitive sense of "become like a ball, form a compact cluster" is from 1713; that of "to copulate" is first recorded 1940s in jazz slang, either from the noun sense of "testicle" or "enjoyable time" (from ball (n.2)). Related: Balled; balling.
ball (n.1) Look up ball at Dictionary.com
"round object, compact spherical body," also "a ball used in a game," c. 1200, probably from an unrecorded Old English *beal, *beall (evidenced by the diminutive bealluc "testicle"), or from cognate Old Norse bollr "ball," from Proto-Germanic *balluz (source also of Dutch bal, Flemish bal, Old High German ballo, German Ball), from PIE root *bhel- (2) "to blow, inflate, swell" (see bole).

Meaning "testicle" is from early 14c. (compare ballocks). Ball of the foot is from mid-14c. Meaning "rounded missile used in warfare" is from late 14c. A ball as an object in a sports game is recorded from c. 1200; meaning "a game played with a ball" is from mid-14c. Baseball sense of "pitch that does not cross the plate within the strike zone" is by 1889, probably short for high ball, low ball, etc.

Ball-point pen is by 1946. Ball of fire when first recorded in 1821 referred to "a glass of brandy;" as "spectacularly successful striver" it is c. 1900. Many phrases are from sports: To have the ball "hold the advantage" is from c. 1400. To be on the ball is from 1912; to keep (one's) eye on the ball is from 1907. Figurative use of ball in (someone's) court is by 1963, from tennis.