What is the purpose/people’s intent when davening at the grave of a Tzaddik

I understand the grave of a tzaddik has more kedushah than that of an average person, but when people are davening what are they thinking about? Are they davening to the tzaddik? Are they davening to HaShem but hoping the kedushah of the tzaddik will make their Tefillah more likely to be answered? If the former, is this not idolatry? Been having a difficult trying to understand the intention behind this practice, any thoughts would be appreciated

Edit: Follow up question – How is davening at a tzaddik’s grave different than asking an alive tzaddik for a Brocha