Put at its simplest, a sample is part of a larger population. We all form part of a population: the population of the United Kingdom, of the town where we live etc.,.
Every so often, we may be stopped in the street by someone holding a clipboard. They may ask us a series of questions, or invite us to go and try a new dessert...
What these people are doing, in fact, is sampling. They are taking a small group of people, chosen at random from the passers-by.
Because the interviewees are selected at random, they are taken to be representative of the population as a whole, and conclusions about the wider population can then be drawn by the use of statistics.
And, the basis of statistics is probability theory.