The paradox is well described here: http://plato.stanford.edu/entries/russell-paradox/
In brief, the paradox is a result of this set, this formulation from wikipaedia:
" Define Naive Set Theory (NST) as the theory of predicate logic with a binary predicate \in and the following axiom schema of unrestricted comprehension: \exists y \forall x (x \in y \iff P(x)) for any formula P with only the variable x free. Substitute x \notin x for P(x). Then by existential instantiation (reusing the symbol y) and universal instantiation we have y \in y \iff y \notin y a contradiction. Therefore NST is inconsistent. "