Firstly, check that you understand how this relates to the previous line. It is simply making the subsititution
The notation appears to be a conditional pdf for Y, ie (very loosely*):
That is to say, in very loose terms* it is telling your the conditional probability of Y|X, if the parameter value is equal to theta. The parameter value has to be included because it made the substitution , which will be different for every possible value of
*in fact, pdfs do not give probabilities, but thats a seperate topic...