One of the major goals of current string theory research is to construct a solution of string theory that contains the particles that actually exist in our universe.
String theory started out as a theory to explain particles, such as hadrons, as the different higher vibrational modes of a string. In most current formulations of string theory, the matter observed in our universe comes from the lowest-energy vibrations of strings and branes. (The higher-energy vibrations represent more energetic particles that don’t currently exist in our universe.)
The mass of these fundamental particles comes from the ways that these string and branes are wrapped in the extra dimensions that are compactified within the theory, in ways that are rather messy and detailed.
For an example, consider a simplified case where the extra dimensions are curled up in the shape of a donut (called a torus by mathematicians and physicists), as in this figure.
Strings wrap around extra dimensions to create particles with different masses. A string has two ways to wrap once around this shape:
A short loop around the tube, through the middle of the donut
A long loop wrapping around the entire length of the donut (like a string wraps around a yo-yo)
The short loop would be a lighter particle, while the long loop is a heavier particle. As you wrap strings around the torus-shaped compactified dimensions, you get new particles with different masses.
One of the major reasons that string theory has caught on is that this idea — that length translates into mass — is so straightforward and elegant. The compactified dimensions in string theory are much more elaborate than a simple torus, but they work the same way in principle.
It’s even possible (though harder to visualize) for a string to wrap in both directions simultaneously — which would, again, give yet another particle with yet another mass. Branes can also wrap around extra dimensions, creating even more possibilities.