String theory refers to any one of five specific theories that attempts to unify the four fundamental forces: electromagnetism, strong nuclear force, weak nuclear force, and the most difficult of them all, gravity, via oscillatory dimensional analysis. In other words, it attempts to mathematically describe the universe as if its foundation were based on strings, where the strings that are vibrating correspond to the number of observable dimensions.
The five string theories in and of themselves were all headed in the right direction, but lacked completeness. Therefore an all-encompassing "Theory Of Everything" (TOE) that attempts to unify the five string theories was proposed and is the current leading candidate for a TOE. This theory is called M-theory, and only works if the universe consists of 11 separate strings. The main problem with M-theory, as well as with all of the string theories, is observable evidence, of which there hasn't been any. This is why the search for the Higgs boson at the LHC at CERN is so important. If it's found, theoretical physicists can collectively breath a little easier because that means they are on the right track with M-theory. If it isn't found, that means they're back to square one.
String theory attempts to unite quantum mechanics and general relativity so we can make sense of the universe on all scales, at any place or time, large or small without breaking down.
String theory does this by doing away with the idea that subatomic particles are point-like -- instead replacing that idea with tiny vibrating bits of energy, called strings.
They're so small, that if you enlarged a single atom to the size of our solar system, a string would be the size of a tree on earth. These strings are said to "vibrate" at different rates and that the "notes" (or different vibrational frequencies) give rise to the different properties of quarks and atoms.