String theory is a physical theory that attempts solve several outstanding problems in modern physics.
One problem deals with the unification of the fundamental forces of nature.
Ever since electricity and magnetism were found to be different manifestations of the same force, people have wondered if all the forces of nature are related somehow.
We all know that Einstein's general theory of relativity describes gravity in terms of space-time geometry. Wouldn't it be great if we could describe all the fundamental force of nature using geometry too.
This is one problem string theory is attempting to solve.
Another problem deals with fundamental particles.
We all know about protons, electrons, and neutrons, but there are also a lot of other particles that don't seem to have much to do with anything.
Why do they exist?
How are they related?
Why do they have the physical properties they do?
These are all questions that will hopefully be answered by the string theory.
Lastly, the main reason the string theory was created was to solve a math problem in classical/quantum electrodynamics. The equations describing the electric field end up with some technical problems that ultimately can be traced to the fact that we are trying to describe point like particles.
String theory just gets rid of the point like particles and replaces them with strings vibrating in extra dimensions of space-time.