Like the first game,
Naruto: Uzumaki Chronicles 2 doesn't follow the events of the TV series. Instead, the game's storyline is an original adventure taking place sometime after the Fifth Hokage has taken her station. Again, the exact timing doesn't really fit into the story anywhere, but that's okay since this story is still good.
After returning from a mission, Naruto runs into the Sand Ninja Kankuro who has come to the Hidden Leaf Village in order to warn the town of a clan that is looking for something called Spirit Orbs in order to revive an ancient evil. This clan uses specialized puppets to do their biddings and the evil they are trying to revive is known only as The Master Puppet.
Where most Naruto games are fighters, the Uzumaki Chronicles games are more of a 3D action/adventure line where you will enter a room, fight a bunch of enemies and advance into a new room full of baddies. Enemies drop various items as well as balls of health, chakra and virtue (basically experience points) and as you progress in the game, the various characters you play as get stronger.
Naruto will be the main character that you can play in pretty much any of the missions, but he is often accompanied by one or two other characters from the show (like the aforementioned Kankuro or the newly promoted Shikamaru).
One of the most notable differences between this game and the last is its use of the multiple-playable characters. In the first game, you had a second character, but it was a pretty useless feature that felt tacked-on and was only useful when it was required to get past the mission. In Uzumaki Chronicles 2 on the other hand, the ability to use and switch between your characters is really fluid and very integral in the overall gameplay.
The main mode of this game is Story and that is the one involving the clan of puppet masters. The other mode you will spend a lot of time in is Missions. These are much smaller events that you can use to level up specific characters in case any of your playables aren't quite where you need them to be in order to complete a part of the story.
Skill Plate and Shop Modes are used to customize your characters. In the shop, you can buy items, equipment and other effects that will help in your story, while Skill Plate can be seen as your character's inventory. Here you can arrange skills and ability modifiers on a pattern specific to that player. If you can fit the skill on the plate and that skill is available to the character, then you can use it.
Naruto: Uzumaki Chronicles 2 offers a 2 Player Battle Mode that lets players go head to head with customized or pre-built unlocked characters. Unfortunately, this is the game's least fun mode. Unlike most Naruto games, this isn't a fighter in its roots, and because of this, when the game tries to be a fighter, it feels clumsy and awkward. But if you wanted to play a Naruto fighter, there are a good bit of other choices out there.