Why string theory?
The quantum mechanical description of the world is incomplete as the Schrödinger equation is not Lorentz invariant and therefore fails to describe relativistic particles. Including special relativity into the frame of quantum mechanics leads to Dirac's equation which is Lorentz invariant but has yet another problem. It predicts creation and annihilation of particles out of empty space. To circumvent this unphysical process relativistic quantum field theory and quantum electrodynamics have been developed. There this particle creation and annihilation are interpreted as intermediate virtual processes that occur in interactions between real particles and can be illustrated in Feynman diagrams as internal lines between the interaction points of incoming and outgoing particles. Here a severe problem seems to emerges. In the attempt to calculate scattering processes divergences appear due to the point-like structure of the interaction "region". To some extent one can get rid of these divergences by a redefinition of the parameters of the theory, such as mass or charge. This leads to renormalizable quantum electrodynamics, quantum chromodynamics and electroweak theories, which according to Grand Unified Theories (GUT) are different low energy realizations of a single force. Gravity, however, is non-renormalizable and thus cannot be described consistently in the frame of relativistic quantum field theory. This is where string theory enters the stage.
In string theory the fundamental objects are 1-dimensional strings rather than 0-dimensional particles. The notion of the 1-dimensional worldline of a particle is replaced by a 2-dimensional worldsheet swept out by the string as it evolves in spacetime. In this frame the interaction points of quantum field theory are replaced by smooth interaction surfaces. The fatal 0-distance behaviour hence becomes irrelevant. Furthermore string theory predicts a massless particle of spin 2, the graviton. String theory hence provides a promising candidate for a theory of quantum gravity, the formulation of which remains the major ingredient for the Unification of all fundamental forces in the Theory of Everything (TOE).