DVC members are eligible to buy APs at a discounted rate - $100 off the theme park and I think $125 off the premium AP. The discount is only good for members and their family members living at the same address. So a grandma living with the member is eligible but a member's grown child living elsewhere is not.
There is no discount on dining plans per se, but so far DVC members are not being charged the peak season upcharge on the DDP.
There are also other dining discounts available to DVC members (10-20% at some restaurants) and some small discounts on water park and special event tickets.
DVC members pay the same price as everybody else for the Dining Plans, and there is no "Free" DDP for DVC points stays. But we have two advantages: 1) we don't have to purchase park tickets, and 2) we pay the regular price during those peak periods when DDP jacks up their prices.
ETA: Tara's informatiion on tickets above is more complete and more accurate than mine.
Keep in mind, though, that these are perks, not guaranteed to DVC members. They are here today, and could be gone tomorrow with the stroke of a pen. Perks do come and go, often without any prior notice.
If you are considering purchasing, ignore all mention of perks because they have literally gone away overnight. If you don't believe me, ask the dozens of DVC members who parked their cars with free valet service at night and woke up the next morning to find they owed $10 and would be charged for each night!