When you're talking about an action, a decision, a mistake, a way of thinking, etc. you sometimes need to express who did it. You can do that using "on ___'s part":

It was a dumb mistake on our part.

This means "We made a dumb mistake."

There was no attempt on his part to misrepresent anything or to cover anything up.

This means "He didn't try to lie or hide anything."

Using "on ___'s part" sounds intellectual. You use this phrase when you're discussing or analyzing something.