The website is to initially include the following information:
As the semester continues, you will be adding
You should develop your concept to a degree that you all agree on it. The concept should be specific enough that you are sure that the client, team members and professor will read it and understand it the same way. The concept should outline the goal of the game and roughly how it will work. This description need not be much more than the key mechanisms that are to be used. The goal is to distinguish at the level of whether you are building an RPG, a first person shooter, or a puzzle-solving game, not a complete level design.
Here are examples of what I would expect in a concept statement for Tetris and Angry Birds.
Tetris: Blocks of 4 tiles in different configurations fall and the user needs to turn and move them in order to fill the spaces available at the bottom. When a full row of tiles is created it is removed. The game ends when the tiles reach the top of the screen.
Angry Birds: There are different types of birds with different capabilities. The player uses a slingshot to launch the birds to kill the green pigs. Levels of the game continue to get harder arrangements to kill the pigs. Player is awarded 1-3 stars depnding on how many birds it took to eliminate all of the pigs.
The template for the design is very comprehensive. Some of the elements will not be relevant to your game. If they are not, you do not need to create something. Simply stating that it is not relevant and why is all that is needed.
For a more detailed template, you might be interested in looking at this one provided by Chris Taylor from Runaway Studios.
The design document includes elements of a traditional software design document. This is not as complete a software design document as would be requested in a software engineering class. It is the fundamental elements. A description of what is needed is given in Software Design Document. If you need more detail, you can find a more general discussion on the Software Design Document page.
The initial design document that is due at the same time as the concept should identify the most important elements of the game and fill those in. Ignore everything else.