"sphere, globe, ball," c. 1400, from Old French boule "ball," from Latin bulla "round swelling, knob" (see bull (n.2)). Meaning "large, solid ball of hard wood used in the game of bowls" is from mid-15c.
"testicles," early 14c., from plural of ball (n.1). See also ballocks. Meaning "courage, nerve" is from 1928. Balls to the wall, however, probably is from World War II Air Forces slang, from the ball that topped the aircraft throttle, thrust to the bulkhead of the cockpit to attain full speed.
Ball-busting "difficult" is recorded by 1944; ball-breaker "difficult job or problem" is by 1954. Ball-buster, disparaging for "dominant female, woman who destroys men's self-confidence" is from 1954; ball-breaker in this sense is by 1970 (of Bella Abzug).
1590s, transitive, "to form into a ball, to gather into a ball or round body," from Latin conglomeratus, past participle of conglomerare "to roll together, concentrate, heap up," from assimilated form of com "with, together" (see con-) + glomerare "to gather into a ball, collect," from glomus (genitive glomeris) "a ball, ball-shaped mass," possibly from PIE *glem- (see glebe). Intransitive sense of "to come together in a rounded mass" is from 1640s. Related: Conglomerated; conglomerating.
1779, "the hitting of two or three balls in succession by the cue ball at a single stroke," a shortening and alteration of carambole (1775), from French carambole "the red ball in billiards," from Spanish carombola "the red ball in billiards," perhaps originally "fruit of the tropical Asian carambola tree," which is round and orange and supposed to resemble a red billiard ball; from Marathi (southern Indian) karambal:
If the Striker hits the Red and his Adversary's Ball with his own Ball he played with, he wins two Points; which Stroke is called a Carambole, or for Shortness, a Carrom. ["Hoyle's Games Improved," London, 1779]
"gathered into a ball or rounded mass," 1570s, from Latin conglomeratus, past participle of conglomerare "to roll together, concentrate, heap up," from assimilated form of com "with, together" (see con-) + glomerare "to gather into a ball, collect," from glomus (genitive glomeris) "a ball, ball-shaped mass," possibly from PIE *glem- (see glebe).