If you are faithful and devoted to someone or something, you're loyal. If you refuse to buy milk from anyone other than Farmer Jones, then you're a very loyal customer.
Someone who is loyal is reliable and always true, like your trusty dog. Loyal comes from the Old French word loial which means something like "legal," but if someone is only loyal to you because the law requires him to be, that's not true loyalty, which should come from the heart, not a contract. A loyal friend supports you all the time, no matter what. You can also be loyal to an idea, like the People's Revolution, or girl-power.