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.
Compare similar use of Modern English certainly, absolutely. Used in Old English only at the end of Gospels, otherwise translated as Soðlic! or Swa hit ys, or Sy! As an expression of concurrence after prayers, it is recorded from early 13c.
c. 1600, "exact correspondence in substance or nature," from French coincidence, from coincider, from Medieval Latin coincidere, literally "to fall upon together," from assimilated form of Latin com "with, together" (see com-) + incidere "to fall upon" (from in- "upon" + combining form of cadere "to fall," from PIE root *kad- "to fall").
From 1640s as "occurrence or existence during the same time." Meaning "a concurrence of events with no apparent connection, accidental or incidental agreement" is from 1680s, perhaps first in writings of Sir Thomas Browne.