Bitcoin/litecoin

the video regarding bitcoin and litecoin inspired me to research the topic, and i have a query which i have not been able to resolve:

what is the gpu actually doing when it is "mining for coin" and "solving blocks"?what is the processing power being used for?

P.S. also your beard inpsired me to grow out my own. best decision i ever made! 

Simply put, its doing multiplication. The GPU is doing millions of multriplications every second in an attempt to find numbers that multiply together to make another number. You can think of it as factorisation by trial and error.

This is a bit over-simplified, but basically the GPU is trying to find two extremely large numbers that multiply together to give another large number. This is then recorded as a unique solution and the block is solved.