Violating a Maxim
Violating a maxim is when you break one of Grice's Maxims on purpose, but you don't want anyone else to notice. You're hoping that the other people in the conversation will think you haven't broken any maxims at all, so they won't interpret any hidden meanings in your words. We call a hidden meaning like this an 'implicature'.
Here's an example of violating the maxim of quantity.
Let's say that a student hasn't done the homework. They just handed in a blank sheet to the teacher. They then have this exchange:
Teacher: Did you hand in the homework?
Student: I uploaded the sheet to Google Classroom, yes.
Well, they wouldn't be lying. They actually did post the sheet to Google Classroom. But since the teacher is asking about the homework, and not just the sheet, they aren't providing enough information. It's also clear that they're trying to deceive the teacher. So, we'd say this is a violation of the maxim of quantity.
It edges into the maxim of manner, too, since they're kinda over-explaining things!