early 15c., "collide, clash in hostility," from Latin concurrere "to run together, assemble hurriedly; clash, fight," in transferred use, "to happen at the same time," from com- "together" (see com-) + currere "to run" (see current (adj.)). Sense of "to coincide, happen at the same time" is 1590s; that of "to agree in opinion" is 1580s in English.
["CONCUR, A Language for Continuous Concurrent Processes", R.M. Salter et al, Comp Langs 5(3):163-189 (1981)].