To cull means to select or gather. If you decide to make a literary anthology, you must cull the best possible stories and then arrange them in a pleasing manner.
When you use cull as a verb, the things you gather can be the good or bad ones from a group. In your garden, you can cull the good vegetables for dinner, or the rotten ones for the compost pile. In fact, often no judgment of quality is made, as when you cull information from the Internet for your next research project. The sorting through will come later. However, if you use the word as a noun, a cull is a selection of things you intend to reject, often in reference to a group of animals. An outbreak of a disease such as foot-and-mouth disease can cause authorities to order a cull of farm pigs.