Explain Fixed Pint Combinator

Im stupid, can someone explain to me what the lambda calculus expression for Y combinator: Y = λf·(λx·f (x x)) (λx·f (x x)) means?

ok thank you I get that now, but what I still dont get is where is the fixed point being returned? I mean if I do Y(g(x)) with g(x)=x^2 where and how along the execution does the solution 1 arises