A tenant is someone lives in a place owned by someone else, usually paying rent. If you play your music loud and let the cat pee in the corner, your landlord will not think that you're a very good tenant, and probably won't renew your lease.
Tenant is often used to mean "renter," but it can mean anyone who has the right to live in a particular place, either because he signed a lease, which is a rental agreement, because he owns the land, or because government gave him a title to it. If you live in a big apartment building, you should be aware of your rights as a tenant, which usually include things like having heat in the winter, and proper fire escapes.
