Acceptance is taking something given to you. You might be relieved by your friend's acceptance of your apology for accidentally riding your bike over his foot.
An acceptance of someone or something is also an indication that you approve of or believe in it (or them). If you dye your hair green and wear a suit made of bear fur, gaining your grandmother’s acceptance may prove difficult if she's a conservative dresser and an animal lover. In legal terms acceptance is language signifying consent to the terms of an offer, leading to the creation of a contract.