Analog is a varying voltage (or power level depending on where in the system you look at it). Because the information is transmitted as a varying signal, it is suseptable to noise (snow), ghosts (reflections) and can only handle one program stream at a time.
Digital is numbers, like computer data. As such, as long as the receiver can make out the numbers, it can correct for any transmission problems like noise and reflections. It will assemble a perfect picture every time. Also, because it's data, many programs can be woven into the data stream. The receivers will just pick out the data packets it needs on the other end.
There are always problems getting vast numbers of people to adopt a new and different technology. It's not familiar, and there is a learning curve. I can remember the early days of cell phones when people needed instructions on how to place calls! Ten years from now, we will wonder what all the fuss was about.
Comcast cable is a bit of a different animal. The transition that is due in February only affects over the air broadcasts one would get with an antenna. Cable companies can do pretty much what they want and the only quality of service standards they must meet art what the customers will let them get away with.
ADDITIONAL:
Comcast is (supposed to be) a close system meaning that, within the cables, it is it's own world. If they can't make it work, complain, cpmplain, complain. You are paying for a working system, demand it.