Adam has a good explanation, but I'll add mine:

Statistics are a way of guessing what the distribution of data is in a column. So if you have age, SQL "samples" the data and gets some idea of how many people are < 10, 11-20, 21-30, etc. Note these are my numbers, not really what SQL would use. It would just have an "idea" of the distribution. That way it can "guess" whether an index will help the query run quicker or if it's better to just scan the table.