I have read about functional programming which is stateless, gives the same result invocation after invocation, about closures and other related concepts.

I still feel that I have very little idea what these things are about.

Thinking about this, right now, I feel complete in C, C++, and Java. Any programming problem and I start thinking in one of these languages. So, I never feel and understand the need for functional languages.

A good starting point therefore would be to try to understand some things that are not possible in imperative languages but possible in functional languages. I feel unless I understand where exactly functional languages fit inside my already complete world of C, C++ and Java, I would never be able to appreciate and understand them.

So, can somebody help me understand the real need for functional programming? Where exactly do they fit in?