When you and someone else have agreed on something and that agreement is both binding and enforceable by law, you have a contract. When you rent an apartment, you and your future landlord sign a rental contract.
You can also use the word in this sense as a verb meaning "to hire." Wouldn't you like to contract someone to clean your room for you? In other verbal uses of contract, place the accent on the second syllable — kun-TRAKT. If you contract a disease, you catch it, but only use this if it's something serious. You catch a cold, but contract malaria. Contract also means "shrink." When the economy contracts, consumers stop buying things, and people lose their jobs, and if you freeze water, it contracts too.