Each mode has a different field distribution, which implies different impedance, group delay, etc.
The 'selection' between the propagating modes is usually done by proper design of the feeding network. For example, in a rectangular waveguide the relevant propagating modes can be obtained by placing the pin of the excited coax cable in the right places (as long the frequency is high enough so they propagate). Other modes may still be excited, however the amount of energy of these modes is controlable and usually low.