A contract is a legal agreement [a formal understanding that is enforceable by law] between two or more parties that outlines the terms and conditions [pecific details and rules that both parties agree to follow] of a specific arrangement or transaction.
For example, when you sign a lease agreement [a contract between a tenant and a landlord that outlines the rental terms] with your landlord, you are entering into a contract that states the terms of your rental arrangement.
Very Simple Definition:
A contract is a formal agreement between people that is like a promise, but it has to follow specific rules.
For example. when someone rents a house, they make a contract with the landlord [owner of the house] to be allowed to live there as long as they keep paying.