<p>Can anyone tell me, where on the web I can find an explanation for Bron-Kerbosch algorithm for clique finding or explain here how it works?</p>

<p>I know it was published in "Algorithm 457: finding all cliques of an undirected graph" book, but I can't find free source that will describe the algorithm.</p>

<p>I don't need a source code for the algorithm, I need an explanation of how it works.</p>

Try finding someone with an ACM student account who can give you a copy of the paper, which is here:
http://portal.acm.org/citation.cfm?doid=362342.362367
I just downloaded it, and it's only two pages long, with an implementation in Algol 60!