You can show them (Your Ninjas) to the world, and you can have there your second team, like Kyubi Event team.

As said above... I use lazy wind team (Wind Main, Karin, Kurenai, Hinata) as my main team and use Naruto, Guy and Tenten for Kyuubi, so it's good to have them at hand.
Some others use it just to show of their rares that they never use on their main team lel

lol yeah^^

It's there for certain battles where the line up option shows up before the battle starts and you can then move your lineup around how you see fit, with the option to swap in any of those 3 extra ninja.