The quantity 
is called the conditional pdf.
The constraint that 
simply means that the r.v.'s 
and 
are not mutually exclusive, meaning there
is some probability that both 
and 
will occur together.
Note that if x and y are independent r.v.'s, then 
and 
reduce to the univariate pdf's for x and y:
and therefore for independent pdf's we find that the bivariate pdf is simply the product of the two univariate pdf's:
