When conducting a study, a researcher selects a relatively small group of participants (a sample) from an entire population of all possible participants (for example, selecting college students at a couple of colleges from all college students in the world). Ideally, the researcher would have participants with characteristics that closely match the characteristics of the whole population - this is called having a Representative Sample.
This is important if you want to extend the findings of the study to a larger group of people, not just those in the study. For example, imagine you are at the supermarket picking out grapes. There are red, green, small, large, and globe grapes. In a representative sample you would have an equivalent number of each type of grape. You could then taste them all and make generalizations about all grapes just from tasting these few because your sample represents the larger population.