String theory (M theory, Superstring theory) is an attempt to unite Einstein's general theory of relativity with quantum mechanics. Another approach is called loop quantum gravity.
Quantum mechanics is based upon the uncertainty principle postulated by Heisenberg. It also rests upon the observation that energy, momentum, spin, and other properties are not infinitely divisible — they come in chunks called quanta. It is possible that space and time are not infinitely divisible as well, and that the divisibility of space ends at 10-35 meters, the Planck length. The smallest equivalent time unit is 10-43 seconds — the time it would take light to travel a Planck length.
The general theory of relativity is a classical theory based on the idea that mass can be concentrated at a true point of zero size.
These two major theoretical pillars are incompatible at this basic level. Attempts to combine classical relativity and quantum theory lead to nonsensical results containing infinities and probabilities greater than one. Superstring theory postulates that all particles are vibrating strings of small but finite size. Different particles are defined by their unique vibrational patterns. Because strings are postulated to be finite in size and not true points, the theory allows quantum mechanics and general relativity to coexist without the singularities that result from point particles.
There are several excellent books that explain the concepts and current status of these theories using a non-mathematical approach: