I've been doing some research into this lately. You get an actual book of vouchers. Here's the list of what you get for a 6 day plan:
Mickey's 6 Days of
Disney Dining Plan
15 Disney Dining choices per person.
Adult/Junior Meals included
Character Breakfast 1
Character Lunch 1
Character Dinner 1
Breakfast in the Park 2
$5 Voucher 3
$10 Voucher 4
$15 Voucher 3
Child Meals included
Character Breakfast 1
Character Lunch 1
Character Dinner 1
Breakfast in the Park 2
$5 Voucher 5
$10 Voucher 4
$15 Voucher 1
When you eat at a counter service place in the parks and it comes to $16 or something, you would just tear out a $15 voucher and then pay cash for the rest (no change given, so you'd want to make up the difference with cash rather than giving them too much). The breakfast in the park is at either DL or DCA, at a certain restaurant. You have $8.95 to spend on the breakfast, I think, and it's a counter service place. The character meals can be in the parks or at the hotels, there may be a small additional fee for Goofy's Kitchen. You can use the dollar value vouchers at either counter service or sit down restaurants, with the exception of Ariel's Grotto, The Cove Bar, The Vineyard Room, Golden Vine Winery and the Wine Country Market, all at DCA, I believe. Snack vouchers are valid for any of the snack carts, up to $5 value.
If you're going for 6 days, you don't necessarily have to get the 6 day package. You can get the 5 day and then make it stretch by combining vouchers, etc. Also, I've seen some stories of people who got a dining plan for the same number of days as their trip and then had vouchers left over, which aren't refundable.
I had read that the price of the meal plan comes out to almost the same as individually pricing everything, but my super-budget police didn't get the figures to add up. The tax and tip is included at the character meals, so that may have been the difference.