A sample is a small part of something that either represents a bigger whole or is designed to let you try something out. You might ask to try a sample of an exotic ice cream flavor before committing to buying a whole cone.
Sample comes from the Old French essample, meaning "example." In social science experiments, researchers try to find a sample of people to study that is representative of the intended population as a whole. At the grocery store, you might be given a sample of peanut butter on a little cracker to entice you to buy it. In that case, you are given the chance to sample, or taste, the product.