The dining plan is part of a package (provided you are not staying as a Disney Vacation Club Member) that you can add and it covers your dining for stay.
For every NIGHT that you pay for in your onsite hotel you get:
1 Counter/Quick Service Meal
1 Snack (typically can be used at the snack carts for sodas, ice creams, chips, etc.)
1 Table Service (such as Crystal Palace)
So if you stay 5 nights, you'll get five of EACH things listed above. You are free to use your meal 'credits' as you wish during your stay. For example, you could use all five of your snack credits in one day if you choose.
Some table service restaurants 'cost' 2 credits (such as Cinderella's Royal Table).
Check out the board above titled '
Disney Dining Plan'...there's TONS of information...lists of restaurants participating in the Dining Plan.
Feel free to ask here too...people are super friendly and helpful.