A string is a brane of dimension one higher than an ordinary particle:

where a 1-dimensionalsigma-model may be thought of a describing the dynamics of particles propagating of a target space$X$, a 2-dimensional sigma-model is said to described the dynamics of a string on some target space.

Much of traditional quantum field theory on $X$ may be understood in terms of second quantization of 1-dimensional sigma-models with target space$X$. What is called string theory is the corresponding study of what happens to this situation as the 1-dimensional $\sigma$-model is replaced by a 2-dimensional one.