When you make an ability check, you add a skill die to the roll when you can justify that it falls within one of the 3e skill categories that you are given as part of your background/specialty/theme package. So, for instance, a first level Rogue with the Scout theme adds 1d4 to her ability checks (on a d20) for Disable Device, Knowledge (Nature), Sneak, and Survival. The skill die improves with level, so that at 20th level the Rogue uses all the same skills at 1d12.
This is the basic skill mechanic in the latest playtest packet from 5e. It's pretty simple.
In some ways, the ideas that have been debuting for Next have felt both familiar and avant-garde, and the skill dice mechanic is an example of this. It reminds me of the randomized attack bonuses in 3e's Unearthed Arcana. Many things seem to remind me of that particular rule, I suppose because of the difference that it illustrates between Average Improvement and Incremental Improvement.
These two terms I am using to differentiate between an improvement of +1 per level (Incremental) and an improvement from 1d4 to 1d6 (Average). The former tends to contribute to bonus inflation and min/maxing, the latter… I'm not sure. I kind of like the idea of increasing a die because it allows for definite improvement without marginalizing the random elements. At certain points in 3e, rolling dice became annoying as one acquired enough bonuses to feel 'above' to luck of the die. 4e was built with this in mind, as many hits and damage amounts are rendered automatic. The 'skill dice' system seems to allow for improvement without entitlement, and that's a good thing. It also consciously builds off of the Ability Check system without rendering the former pointless or underpowered, like the 3e skill system did.
One question: what about picking up skills later? I haven't seen many good ideas for this, despite the fact that one assumes that adventurers would develop in new and unexpected ways as they continued their journeys. This would seem to be at odds with a class system, where one's powers at 20th level are assumed to be direct extrapolations of 1st level abilities. I like my Token Proficiencies, but they are just a way to formalize ad-hoc knowledges and special abilities.