As others have said, only on select dates....and the discount is relatively small. For example....the MVMVP tickets purchased in advance by the general public are $67 (plus tax).....the AP discount is $62 (plus tax) so your savings is only $5 off the advance purchase price. Not a big discount, but it can add up quickly for a family.
There are nine dates that do NOT have an AP discount (and 6 of those dates don't have a advance purchase price either).
A good chart to see the price break down is
here.
Some of the other discounts that an AP can get you are 10% off merchandise and food (select stores/restaurants, check Disney's website for the list). And of course, free parking (parking is free to those staying on site, but if you're staying off site without an AP it's $17 a day for cars). If you do a lot of Table Service eating you might also want to look into the purchase of a
Tables in Wonderland card. It gives you a 20% discount at most TS restaurants, but be aware there is a gratuity of 18% added. The card costs $100 so you'll want to estimate your use of TS restaurants to decide if the discount will work for you.
I wouldn't base my decision to purchase an AP on the relatively small discounts it gets you (unless you're a big souvenir purchaser), but more on the savings on parking and admission. For example, a 10 day park hopper is around $440....you can't buy a larger day pass, so if your stay is 12 days it would cost you an additionl $250 for a 2 day park hopper.....so a total of $690. An Annual Pass is only $675, so the break even point is generally recognized if you plan to visit 10-12 days in a 12 month period. There are other factors, such as my numbers above don't include the water parks/etc addition or if your visits were to be, for example 2 one week visits, the savings would be even better. So you'll want to do some math to determine if it's right for you.