String theory is a theoretical model of particle physics which hypothesizes that all matter, at the most fundamental level, is made up of tiny vibrating strings, or loops. According to this model, different particles and atoms would arise from differences in the vibration of these strings, much like guitar strings make different sounds depending on the pressure you apply to them. This model is an alternative to the Standard Model of particle physics (the most widely accepted model) which operates according to the laws of quantum mechanics. String theory is not yet supported by empirical evidence because scientists have not yet found a way to actually test the theory. Consequently, many physicists are skeptical of this model; however, theoretical research continues to demonstrate promise for string theory.
M-Theory was born out of string theory and is considered to be an extension of this model. M-Theory accepts the assumptions of string theory, but adds the hypothesis that there are eleven dimensions of space rather than the three we are currently able to observe. It is difficult to understand the reasoning behind this without delving into the complex underlying mathematics, but essentially M-Theory is a modified version of string theory.