To tire is to grow weary or bored with something. As a noun, a tire is the large, rubber ring that surrounds a car's wheel. You might tire from the hard work of changing a flat tire.
When you tire, you need rest, or sometimes just a break: "When I tire of working on my homework, I like to read a book or watch TV for a while." As far as etymology goes, the verb is completely unrelated to the noun. The verb comes from an Old English word meaning "to become or make weary." The wheel-covering tire, on the other hand, was originally a shortened form of attire, "clothing or apparel," from the idea that a tire is, in a sense, clothing for a naked wheel.