The zero tolerance policy in schools is basically where the school gives the student a harsh punishment for breaking certain rules in the school.
Usually the school will suspend or expel the student from school for certain rule violations or even call the police if the rule being broke is severe enough to warrant the police.
Under the zero tolerance policy the schools harsh punishment applies regardless of the circumstances.
The schools zero tolerance policy is a very strict enforcement of regulations and bans against behaviors or the possession of items deemed undesirable by said schools.
Break any of those rules then you'll get into severe trouble so avoid breaking those rules.