Snow's basic thesis was that the breakdown of communication between the sciences and the humanities (the "two cultures" of the title) was a major hindrance to solving the world's problems. This is combined with some criticism of the British education system and some broad suggestions as to how to change it. It is hard to see why quite such a fuss was made over Snow's lecture at the time; as he himself was the first to admit (in the second work), nothing he said was particularly original. Perhaps the time was just ripe for a controversy.
Snow's ideas are clearly dated (his view of science and the arts was formed at Cambridge in the 1930s), and his viewpoint is very simplistic in places (his somewhat naive assumption of the ability of science to solve the world's problems is perhaps the most notable). Any communication problem between the arts and the sciences is now subsumed by a much more general fragmentation of human learning, a fragmentation which is actively lauded by many. The introduction (which is in many ways more interesting than the actual text) discusses these issues and others.
While no longer essential reading, The Two Cultures still warrants attention from anyone interested in the history of ideas. Coupled with an impressive introduction and released under Cambridge University Press' affordable Canto imprint, this is definitely a worthwhile volume.