What exactly is competitive programming

If you want to take your programming to next level, you must have a strong mathematical background. Every super-coder has a really strong mathematical background. And because of this they are able to solve complex problems very easily and in low space & time complexity (O(1)). Though you need to put various logics behind every problem but math acts like a catalyst(more than a catalyst). 
To achieve good and competitive programming skills you need to practice a lot (atleast 8+ hrs a day). There are plenty online judges(Codechef, SPOJ, Hackerrank,etc) where you can find lots of questions under various domains to practice. Just sign up and start your journey of <coding/>. Also go through Design Analysis & Algorithmsby Cormen,Rivest,Stien, here you can find different ways to solve different types of problems.
Remember one thing "People very often mistake programming competitions for the measure of being a great programmer in general. The truth is that neither one implies the other." 

Keep calm and keep doing!