late 14c., "hurt, harm, injury, pain;" also "breach of the law, wrongdoing; transgression against God, sin;" also "the causing of displeasure, act or fact of wounding the feelings of or displeasing another;" also "displeasure, annoyance, umbrage," from Old French ofense "offense, insult, wrong" (13c.) and directly from Latin offensa "an offense, injury, affront, crime," literally "a striking against," noun use of fem. past participle of offendere (see offend).
Meaning "action of attacking" is from c. 1400. Sporting sense of "the team on the attack, at bat, with the ball," etc. is by 1894.