"Having those extra dimensions and therefore many ways the string can vibrate in many different directions turns out to be the key to being able to describe all the particles that we see"

This quote by Edward Witten is referring to the idea of string theory, which is a branch of physics that tries to describe the fundamental nature of matter and energy. String theory recommends that all particles are comprised of small vibrating strings, which the various ways these strings can vibrate is what provides particles their various homes. The quote suggests that the key to understanding the particles we observe in nature is the fact that strings can vibrate in several instructions, due to the presence of additional dimensions. This indicates that the exact same string can vibrate in different methods, generating various particles. This is why string theory is so essential in physics, as it supplies a method to discuss the range of particles we observe in nature.