It is very confusing and very expensive!
DS had this last christmas and was bitterly disappointed and sold it a few month back. He said it was boring 
Basically you get a platform which you put the characters on. Once they are on the platform they are in the game.
There are 2 modes to playing - toybox and playset.
Each playset comes with 2 characters and the playset piece.
In playset mode you have to put a playset piece and the corresponding characters on the platform to play. Example - disney cars. You have to put the playset piece (trophy) on the platform then you can put mater or lightening on the platform and play the disney cars game.
In playset mode you can only play the right characters with the game ie you cannot put buzz lightyear into the disney cars game.
If you want to play toy story then you have to buy the playset pack which has the playset piece and the 2 toy story characters.
Toybox mode is a bit more fun.
All characters can play in toybox mode. You don't need a playset piece for it. You could play mickey and buzz lightyear together in toybox mode.
There are different modes in toybox such as building mode, driving mode, combat mode and some others. You basically have to build the world in order to play. So in driving mode you have to build your own racetrack.
When you play a new character in toybox mode, you get to open a treasure chest which unlocks more features for you to build with.
In toybox mode you can also get power discs. You get 2 in a pack and they unlock different coloured backdrops or give power ups to the characters.
Basically the more you buy the more you get.
On Wii you can only play one character at a time, there is no multiplayer option in playset mode but i think you can do 2 players in toybox mode.
The playset's are like traditional computer games where you can complete them. Unfortunately they are quick and easy to complete.
They are now also brought out the 2nd version which is the marvel superheroes version. I believe the disney and the marvel versions cannot be played together fully so you will have to check if your dc want to do both.
You need deep pockets for this game. Each playset is £15 - £30 and each seperate character is £10 minimum.
We ended up with a disney cars playset then DS bought vanellope out of wreck it ralph which he could play in toybox. If the character is a toybox only character then on the packet there is a little toybox logo.
I hope this makes some sort of sense to you. If not i'll try and explain a bit better.