Typically, there is a maximum width that you can run before the tire starts to hit something on the bike. With road bikes using short-reach calipers that's typically about 25mm or 26mm wide. Also note that a wider tire will be greater in diameter than a narrower tire. A bicycle which can handle bigger tires (700X35mm, for example) can typically handle any tire size smaller than the maximum though this is limited by the rim. Actually, rim width limits useable tire size in both directions -- don't put a real fat tire on a skinny little rim and don't put a skinny little tire on a big honker of a rime either. But a with medium sized rim (maybe 22.5mm) can handle tires from about 25mm to about 40mm which is a wide range of sizes.