A congruent number N is the area of a right triangle whose sides are all rational numbers (a number that can be stated as a fraction, not something like pi or e).
For example, consider the right triangle with side lengths 3, 4, 5. The area of this triangle is
. Thus, 6 is a congruent number. The area of a triangle with sides that are any set of the Pythagorean Triples will be a congruent number. I have attached a more precise definition for you from a math blog at UConn (don't let the technical definition confuse you!).