If you have an idea for something, or if you understand something fully, you conceptualize it. You might conceptualize the plan for a big party, but find it hard to conceptualize exactly how the big bang worked.
In conceptualize, you see the word concept which means an idea. Don't think of a simple idea though, like taking a walk. Imagine a complex concept involving many elements, so a little brain work is involved. When you conceptualize, you either create a concept or you grasp one. The idea of man landing on the moon was conceptualized hundreds of years before it was planned or achieved.