early 15c., "a combination for some purpose, cooperation" (a sense now archaic or obsolete), from Old French concurrence (14c.) or directly from Medieval Latin concurrentia "a running together," from concurrens, present participle of concurrere "to run together, assemble hurriedly; clash, fight," in transferred use, "to happen at the same time," from assimilated form of com "together" (see con-) + currere "to run" (from PIE root *kers- "to run").
Sense of "occurrence together in time, coincidence" is from c. 1600. Meaning "accordance in opinion" is from 1660s.