Simply put, contract law is the law that governs contracts. A contract can be written out on paper or just a verbal agreement. The contract is an agreement between two or more people which creates an obligation to do, or not do, something. The agreement creates a legal relationship of rights and duties. If the agreement is broken (breached), then the law provides remedies.
The three factors necessary to create a contract are: offer, acceptance and consideration. One party makes an offer, the second party must accept the offer and there must be consideration exchanged.
For example; Joe offers to buy Steve's car for $1000. Steve accepts Joe's offer. Joe pays Steve $1000 (that's the consideration for the car) and Steve gives Joe the car. If Steve refused to give Joe the car, then Steve has breached the contract.