From your description (breakfast/snack/sit down dinner), it sounds like you're getting the standard plan, aka DDP (
Disney Dining Plan). This comes with 1 QS (Quick/Counter Service), 1 TS (Table Service) and 1 Snack per person per night of stay. Now, we all know this already

, so I'll continue on.
When you check into the resort,
all of your credits will be available for all nights of your stay. So, for example, 3 people staying 5 nights, you will have 15 of each as soon as you check in. If you so desire, you can use every single credit that day (I'd not suggest it though

). These credits may be used in whatever order and amounts (up to the limit on your card, which is the number and breakdown of your traveling party) you wish. They can be used even after you check out, but they will expire at midnight immediately following check-out.
Now, each QS and TS meal covers an Entree, Dessert, and Drink (soft-drinks, sometimes coffee/tea, sometimes bottled water) or an admittance to a buffet/family style/fixed price type of thingy. Prix Fixe menus (fixed price, specific 3 course type menus) are also allowed on the plan in most cases. In fact, if you're good with the offerings (no substitutions), this is a great way to score a covered appetizer on the normal DDP.
There are some special cases as well...
Marrakesh - feasts (similar to the prix fixe menus I describe above) have a surcharge added to them when purchasing with the DDP.
Via Napoli - Most strict when it comes to the dining plan. Does not allow larger pizzas to be purchased with credits (individual only), does not allow sharing on the DDP, extra toppings to the "make your own" pizza will be charged to the guest.
"For 2" - Items that are marked as being "for 2" must be purchased by 2 people on the DDP, they (usually) cannot be split up and served to just 1.
Appetizers (other than included in the prix fixe menus), extra sides, alcohol, and other specialty items will not be covered by the plan and will be charged separate. When in doubt at a particular meal, ask your server or cashier and they'll point the stuff out to you. Also, at most TS locations, you WILL be given a spiel on what's covered and all that. You WILL know it by heart by the time you leave!
I think I covered most everything and probably way more than you wanted to know. Don't sweat it too much though as you'll become well versed after a couple days

.