What exactly are they talking about and what do I have to look forward to?
You have years of future trips to Disney (and its associated properties) freely comp'ed and provided for by your loving and charitable parents, who by the sound of it want to bestow that charity on your children as well.
If you signed papers then it also means they made you owners on the contract giving you all the cool benefits we members get (discounts on Annual Passes and special events for you and anyone living in your house, periodic newsletters, invites to members-only events, access to the online planning and information center).
If you didn't sign anything than that means your parents intend to will the property to you. Once they're gone, you can continue to take your grown children, visit yourself or possible take your grandchildren up until 2054 (47 years from now). You'll have to pay the annual dues (currently $4.64 per point at SSR) but there's no upfront cost. Your parents have already paid that for you ($80-100 per point and expected to rise).
When my dad (a 75 y.o. granddad of 9 rugrats) and I (Auntie Mame of the family) purchased DVC last year, we named all three of my siblings as owners on the contract. Our reasoning was that we wanted to make it something they could easily inherit so the entire family would have a chance to enjoy the magic of Disney. We're the principles and I am designated the one to manage the account with Disney, but we have an open door policy with my sibs. All they need to do to have a Disney vacation is tell us when. My sister and her boys will be joining us in a couple weeks to celebrate birthdays, her anniversary and Halloween Disney style. All she had to do was take off work and buy airline tickets. I did all the planning and calling.
My sister is notorious for never planning anything until the last possible moment. But once she got the latest DVC newsletter telling all about the Halloween parties, she suddenly got very excited. (Very cute too. She called me up to tell me our travel dates coincided with a special DVC member discount date of the Halloween party. Without I beat I told her "Yeah I know. I bought tickets for all of us months ago." It was first announced on the DIS and I jumped like a good Disney planner.) Her boys can't stop talking about their costumes and what rides they're brave enough to try. And my dad and I are just hoping they have a good time.
So relax. Enjoy the gift you've been given and remember to thank your folks. They did this because they love you and your family, and they want to share that quality vacation time with you.