The laws make a given attack or ability illegal to use for the duration of that battle. For example, the judge might make Ice illegal, which makes Ice-elemental spells illegal to use. That one sounds simple of course and isn't too damaging, but what are you going to do when they make White Magick illegal? Or physical attacks? Or items? Your ability to change your team's dynamics based on the current law will affect not just your success in battle, but your rewards upon winning as well.
You are "free" to break the law insofar as the game doesn't outright prevent you from using that ability. However, breaking the law results in two major penalties. First, breaking the law means that any knocked out characters on your team will be unable to be revived through any means, such as Phoenix Downs or White Magick spells.
At the start of every battle, you'll get to choose one Clan Privilege, which is a statboost for your whole team. The second major penalty for breaking the law causes this privilege to stop working. Keeping yourself clean earns not just the privilege, but also some permanent rewards (in the form of items and equipment) after your victory as well. There might be times where you'll want to break the law to make a battle easier, and other times where following the law is literally impossible. This is because the laws are tied to battles, not a cyclical system as they were in Final Fantasy Tactics A2: Grimoire of the Rift. For example, during one quest, the law was "Do less than 50 HP damage."
Most of the time, you'll only break the law because you forgot about it. Still, if it seems like the only way to win is to break the law, do so: a temporarily jailed character is better than a Game Over. Just remember that, once you do, you'll need to watch your team's HP carefully. Also remember that laws do not work both ways. If the law is to make physical attacks illegal, and you hit your enemies with the Berserk status ailment, they would still be able to smack you around freely. This is a major change from Final Fantasy Tactics A2: Grimoire of the Rift, so be aware.