The first Super Mario Galaxy was generally thought of as an amazing game, and was well received by most people. It hearkened back to the goodness of Super Mario 64, and made us almost forget about Super Mario Sunshine. Super Mario Galaxy was superb, as a single player experience, but the less than perfect co-op was disappointing. Player 2's options were seriously limited: shooting star bits, holding enemies, and assisting Mario's jump. While this was great for casual fans, particularly young players, more experienced Mario players wanted more. Super Mario Galaxy 2 has delivered improvements in this respect, though the co-op is still not ideal.
Player 2 has a few new tricks up his or her sleeve, and each of them are extremely useful. Most obvious is the inclusion of an in-game character representing the player. In Super Mario Galaxy 2, the second player is an orange star person, floating along with Mario through his adventure, no longer a nameless star reticule. I know it sounds superfluous, but having an actual avatar of sorts in the game adds greatly to the co-op experience; it feels more like you are a team, instead of just an afterthought. This star person is appropriately named Luma, and has all the same star-shooting and enemy-holding abilities of player 2 in the first Super Mario Galaxy.
One new ability for Luma is collecting coins and other power ups. By holding the star reticule over an item and pressing A, Luma shoots out, grabs the object, and returns it to Mario. This makes collecting 1UPs, coins, and other valuable items far easier. In many cases, Luma is able to easily reach things that Mario would be hard-pressed to get to alone. You'll feel as is Mario couldn't do it without you, and that's sorely needed in a game where Mario is clearly the star (pun intended) of the show.
Luma's interactions go a step further when dealing with enemies. Zipping out at the press of the A button, Luna holds enemies still, allowing Mario to avoid being overwhelmed. Best of all, some enemies can be dispatched by Luma alone! A few vigorous shakes of the controller, and poof, bye bye bad guy! There are a few caveats: certain enemies can't be wrestled into submission by Luma (Bullet Bill, for example), and most bosses can't be held at all. Still, this new ability is extremely useful, especially when the action gets frenetic, as it so often does in Super Mario Galaxy 2.