A breach-of-contract lawsuit will be filed if one party believes that the other party has broken an agreement in a signed contract. Typically, when you sign a contract, you agree to do something. You might agree to deliver something to someone else, you might agree to provide services for that person, or you might agree to pay money in exchange for something.
If either party does not hold up their end of the bargain, then that party could be guilty of a breach of contract. Of course, contracts come in many shapes and forms. Therefore, the exact nature of the allegation can vary depending on what is stated in the contract.