How do you get those emblems? When you fight, there are certain mission that you should complete. If you complete the missions, your emblem will become Law. The game starts with the neutral emblem, wich gradually will become Law or Chaos depending on how you complete the missions. If you kill all the enemies when this is not the mission, then your emblem will become Chaos.
You choose the side you like, the different reputations have different units that will join your army:
If your emblem is Law, El, Ellis, Shane, Jenny, Arby, Richard, and Shim will join your army, while the characters of Chaos won't do it.
If your emblem is Chaos, Ryoukan, Teita, Sonia, Lance, Shelly and Gust will join your army, while the characters of Law won't.
Both of the reputations have good characters and if you want a Chaos emblem you don't necessarily have to kill all the enemies everytime. This way your party will gain the bonuses and you can escape from some battles too. If you kill some enemies and then escape from battle, your emblem will become Chaos.
If your emblem is too close to become neutral, some characters will start to complain about it. Yes, the characters of Law/Chaos have different levels of tolerance to the emblems.
The most untolerant characters are:
-For Law, Shane, Richard and Jenny respectively.
-For Chaos, Lance, Gust and Shelly. Teita is something different: She will leave the group without a warning if your emblem becomes Phantom ^^;
However, there are other characters very tolerant. A good example is Ellis. She will be in your group and just complain when your emblem is Hell hound!

The different emblems also give different endings. There are 4 different endings and you'll get a certain ending:
-When your emblem is Fedain (this one is hard to get).
-When your emblem is Valkyrie, Griffith or Blade eagle.
-When your emblem is Byper, Phantom or Balrog.
-When your emblem is Hell hound or Genocide.