"have bigger fish to fry"   -  means to have more important thing to do than something that else; (имам по-важни неща за правене) 

Синоними: have other fish to fry; have more important fish to fry

Example:

Emma: Please, mom, help me to choose my dress for tomorrow.

Mother: I have bigger fish to fry. somebody has to cook the dinner and feed your little brother.