Zero tolerance is a policy of not allowing any violations of a rule or law. When a school has a zero tolerance policy for tardiness, it means that students are punished the first time they're late to school.
It's most common to use the phrase zero tolerance when you're talking about punishment of some kind. If a city announces that there will be zero tolerance for littering, it means that you will get a ticket if you're caught throwing your burrito wrapper on the ground. It's zero tolerance because a law breaker gets zero warnings or chances before facing some punishment — in other words, the law's enforcer won't tolerate any law breaking, no matter how slight.