There seems to be some mystery surrounding exactly "why" this is, and although duffymo has explained part of it, I'm looking at another post that says:
There should be no reason why 5, 6 and 7 should be rolled more [than 2] since the first roll of the die is a independent event from the second roll of the die and both of them have equal probablity of 1-6 of being rolled.
There's a certain appeal to this. But it's incorrect...because the first roll affects the chances. The reasoning can probably most easily be done through an example.
Say I'm trying to figure out if the probability of rolling 2 or 7 is more likely on two dice. If I roll the first die and get a 3, what are my chances now of rolling a total of 7? Obviously, 1 in 6. What are my chances of rolling a total of 2? 0 in 6...because there's nothing I can roll on the second die to have my total be 2.
For this reason, 7 is very (the most) likely to be rolled...because no matter what I roll on the first die, I can still reach the correct total by rolling the right number on the second die. 6 and 8 are equally slightly less likely, 5 and 9 more so, and so on, until we reach 2 and 12, equally unlikely at 1 in 36 chance apiece.
If you plot this (sum vs likelyhood) you'll get a nice bell curve (or, more precisely, a blocky aproximation of one because of the discrete nature of your experiment).