mid-15c., "communication to and fro," ("In early use exclusively with reference to trade" [OED]), from Old French entrecors "exchange, commerce, communication" (12c., Modern French entrecours), from Late Latin intercursus "a running between, intervention," in Medieval Latin "intercommunication," from intercursus, past participle of intercurrere "to run between, intervene, mediate," from Latin inter "between" (see inter-) + currere "to run" (from PIE root *kers- "to run").
Sense of "frequent and habitual meeting and contact, social communication between persons" is from 1540s. Meaning "mental or spiritual exchange or intercommunication" is from 1560s. Meaning "sexual relations" (1798) probably is a shortening of euphemistic sexual intercourse (1771) with intercourse in its sense "social contact and relations."