There are two main things that claiming jail refers to 1)the location 2) the claiming price of the next start.
The location aspect is fairly straight forward, the primary rule is that when you claim a horse it can't leave the track where you claimed from for 30 days after the claim. This rule changes with the state as some allow you to change tracks, but not leave the state the claim was made in. Additionally the time you're in jail will vary from 30-60 days depending on the states rule.
The second part of claiming jail is that the claiming price of your next start must be more than what you had claimed it for. Meaning if you claimed a horse for $5,000 the next race you run the horse in must have a claiming price of more than $5,000. This is to prevent owners from trying to make easy money by running their horse at a low level knowing it will get claimed after one start.