Numerically, a perfect square is a number that is the product of another number multiplied with itself ( 4 x 4 = 16. 16 is a perfect square).
For trinomials, a perfect square trinomial is a trinomial that is the product of a binomial multiplied with itself ( (2x-5)(2x-5) = 4x^2 - 20x + 25. 4x^2 - 20x + 25 is a perfect square trinomial).
If you know a trinomial is a perfect square going into the problem, factoring it is relatively easy. Just find the square root of the lead term, the square root of the last term, and decide whether a + or - sign belongs in the middle.
For example, in 4x^2 - 20x + 25, the square root of 4x^2 is 2x. The square root of 25 is 5. My solution will either be (2x+5)(2x+5) or (2x-5)(2x-5). FOILing these out (as you should always do to check your answer) we find that the minus sign works.
4x^2 - 20x + 25 = (2x - 5)^2