The bearings are the things that let the wheels and the crank and the fork turn. In their most basic form, they are a set of stainless steel ball bearings of 3/8" or 1/4" in diameter that sit in grease between an axle and a wheel or between a bottom bracket spindle and the bike frame (actually there are two polished bearing surfaces called cones and cups that the bearing contact). The grease around the bearings needs to be replaced periodically (about once per year) to keep the bike operating smoothly. Some high-end parts these days use sealed bearings so they are less susceptible to water penetration, and these bearing cartridges need to be replaced occassionally but should last several years or more.