An elaboration of the term "preparation".

Question

I have always had the desire to be able to solve difficult problems from maths contests but somehow every time I barge upon preparing myself for this ability, to be honest , I end up being pushed down by sense of defeat cause I can't solve most of them and the solution to some of the problems seem like I couldn't have thought of anything like that ever and wonder how anyone could ever come up with such an idea to solve a problem . I go through the posts of people who have been pretty successful at these contests and I get a bit confused when they say that while PREPARING they SOLVED a lot of problems to gain practice and intuition necessary to figure out the methods or tricks to be applied. I want to know what exactly they mean by that , does their problem solving involved learning tricks which they too believe that they couldn't have come up with ? Do they too get stuck and find themselves clueless about some problems ?