String theory is a mathematical framework that replaces point-particles with 1-dimensional objects known as strings, which vibrate at some resonance to create an elementary particle; and is a candidate for a "theory of everything" or a theory of quantum gravity, a reconciliation of quantum mechanics and general relativity; that attempts to describe the fundamental forces and particles.
One of the most notable fundamentals of string theory are the extra dimensions that are required for mathematical consistency. Bosonic string theory, the original model of string theory, requires a 26-dimensional space; superstring theories, the attempts to explain the fundamental forces and particles by string theory, require a 10-dimensional space; and M-theory, the union of all superstring theories, requires an 11-dimensional space. These extra dimensions are compactified at a very small scale (on the order of the Planck length), and our 3+1-D vacuum state (universe) is localized on a brane. The entire space is sometimes called a "multiverse", although it is a completely different view of the multiverse than the many-worlds interpretation of quantum mechanics.
Attempts to create consistent models of particle physics based on string theory is the domain of string phenomenology. The application of string theory to cosmology and cosmogony is known as string cosmology.
As of now, there is no empirical evidence for any strings or extra dimensions, and string theory is sometimes considered a speculative model.