One of three requisites to a valid contract under common law (the other two being an offer and consideration).
A contract is a legally binding agreement between two or more parties which starts with an offer from one person but which does not become a contract until the other party signifies an unequivocal willingness to accept the terms of that offer.
The moment of acceptance is the moment from which a contract is said to exist, and not before.
In Book 9(1) of Halsbury's Laws of England, 4th Edition (2007), the authors, using no less than 13 footnotes throughout the short excerpt, describe acceptance as follows:
"An acceptance of an offer is an indication, express or implied, by the offeree made whilst the offer remains open, and in the manner requested in that offer of the offeree's willingness to be bound unconditionally to a contract with the offeror on the terms stated in the offer."
Acceptance need not always be direct and can, in certain circumstances, be implied by conduct (most notably by handshake, pictured).