To not have squat means to not have anything. Usually it's used in the context of not having resources.
Examples:
When I was a kid, we didn't have squat. We had to sleep on a wooden board.
Compared to that school, our school doesn't have squat! They get a lot of money from sponsors and can afford to buy fancy equipment for the classrooms, and every student has a laptop. Our school doesn't even have computers!