As they move through spacetime they sweep out an imaginary surface called a worldsheet . These strings have certain vibrational modes which can be characterized by various quantum numbers such as mass, spin, etc. The basic idea is that each mode carries a set of quantum numbers that correspond to a distinct type of fundamental particle. This is one of the most attractive features of string theory. It naturally and inevitably includes gravity as one of the fundamental interactions.
Strings interact by splitting and joining.
This essentially accounts for another nice property of string theory. It is not plagued by infinities in the way that point particle quantum field theories are. To compute quantum mechanical amplitudes using perturbation theory we add contributions from higher order quantum processes. Perturbation theory provides good answers as long as the contributions get smaller and smaller as we go to higher and higher orders. Then we only need to compute the first few diagrams to get accurate results.