A string theory is a physical model whose fundamental building blocks are extended objects (strings, membranes and higher-dimensional objects) rather than points. String theories are able to avoid problems associated with the presence of pointlike particles in a physical theory.
The term 'string theory' properly refers to both the 26-dimensional bosonic string theories and to the 10-dimensional superstring theories discovered by adding supersymmetry to bosonic string theory. See conformal field theory and 2D conformal field theory. Nowadays, 'string theory' usually refers to the supersymmetric variant while the earlier is given its full name 'bosonic string theory'. The different superstring theories were discovered to be different limits of an unknown 11-dimensional theory called M-theory proposed by Edward Witten in the 1990s.
The observed 4 dimensions of the universe would seem to be in contradiction with the 10 or 11 dimensions one finds in string/M-theory. This is usually solved in one of two different ways. The first is to compactify the extra dimensions. In other words, this means that the 6 or 7 extra dimensions are so small as to not be detectable in our experience. In the 6-dimensional case, this is done with Calabi-Yau spaces. In 7 dimensions, they are termed G2 manifolds.
Another possibility is that we are stuck to a 3+1 dimensional subspace of the full universe, and we can't get off. This is what is known as a braneworld theory. An interesting byproduct is that these would allow (but not necessitate) observations of quantum gravity effects even at the soon to open Large Hadron Collider at CERN in Geneva. While intriguing, this possibility is not widely believed.
On a more practical level, string theory has led to advances in the mathematics of knots, Calabi-Yau spaces and many other fields. Much exciting new mathematics in recent years has its origin in string theory. String theory has also led to much insight into supersymmetric gauge theories, a subject which includes possible extensions of the standard model.
String theory suffers from two major problems. The first problem is that, as with any current theory of quantum gravity, it does not make any predictions that are currently subject to experimental verification. Thus, it can be neither proven nor disproven, which is a serious problem for any theory of physics.
The second problem is that much of theory is still only formulated perturbatively. While much progress has been made in nonperturbative techniques including conjectured complete definitions in space-time's satisfying certain asymptotics, a full nonperturbative definition of the theory is still lacking.Problems with string theory