Trying to learn math from Wikipedia is like trying to learn English from the dictionary.

As far as the subject matter goes, a convex function can just be thought of as a function with a global maximum/minimum and no other local maximum/minimum. I.E. The derivative is zero in only one place which is the global max/min. These functions can then be easily optimized by taking their derivatives and finding the zero. It is a really nice way to optimize a problem.