Meaning of $\frac{P(X\cap Y)}{P(X)P(Y)}$

Imagine that we have a set $\mathrm{\Omega}$ and X and Y are events that can happen, I mean, $P(X),P(Y)>0$. Then, what does it mean the ratio $\frac{P(X\cap Y)}{P(X)P(Y)}$?

I know that $\frac{P(X\cap Y)}{P(X)P(Y)}=\frac{P(X|Y)}{P(X)}=\frac{P(Y|X)}{P(Y)}$ and if that ratio is equal to 1 then X,Y are independent events, but I can't figure out what exactly it means... please give simple examples.

I found this when reading about lift-data mining.

Imagine that we have a set $\mathrm{\Omega}$ and X and Y are events that can happen, I mean, $P(X),P(Y)>0$. Then, what does it mean the ratio $\frac{P(X\cap Y)}{P(X)P(Y)}$?

I know that $\frac{P(X\cap Y)}{P(X)P(Y)}=\frac{P(X|Y)}{P(X)}=\frac{P(Y|X)}{P(Y)}$ and if that ratio is equal to 1 then X,Y are independent events, but I can't figure out what exactly it means... please give simple examples.

I found this when reading about lift-data mining.