The skill die is a new mechanic in this iteration of the D&D Next playtest. When you make a check for one of your skills, you also roll your skill die (which starts as a d4 at Level 1 and increases thereafter) and add the result to your check. So, your overall skill check becomes an ability check (d20 plus the relevant ability score bonus) plus the skill die result. (Side-note: Rogues can spend their skill die to perform tricks, just as fighters and monks can spend their martial damage dice to perform maneuvers.)
I'm not sure about the skill die. It seems to be a replacement for the static, level-based skill improvement of 4e and the skill points of 3e. In my estimation, both of those earlier models are better. With the static improvement of 4e, you always know what you're going to get, even if you can't customize your skill improvements. The skill point system of 3e allowed players to focus on improving the skills of their choice, at the expense of less-favored skills. The skill die system, however, does not allow for any customization, and the results of skill checks will be more "swingy."
Two data points don't make a trend, but I fear the rise of swingy math in D&D Next. We already have the advantage and disadvantage system, wherein the player rolls twice and takes, respectively, the higher or the lower of the two. Now, with the skill die system, you roll your d20 as part of the check and then you roll the skill die rather than add a static bonus. In any system in which you're rolling more dice rather than adding (or subtracting) static numbers, you're going to have a wider swing in the possible results. In earlier forms of D&D, my character might get cursed and be forced to make an attack roll at, say, -4. If my attack roll total was 16, I'd subtract 4 and get a 12. In D&D Next, that -4 penalty would be replaced by disadvantage on the roll. So I roll twice and get, perhaps, a 19 on one roll and a 3 on the other, and be forced to take the 3. That's a difference of 16! Is a "swingier" system worse? It certainly makes the game more unpredictable.