Standing waves (also called room modes or resonances) form when a sound wave's wavelength fits an even multiple of the room dimension. When the wave and its reflection align in phase, a peak forms; when they are out of phase, a null forms. The result is that bass frequencies are dramatically louder in some positions in the room and nearly inaudible in others.
Room modes are calculated by the formula f = (n × c) / (2L), where f is the frequency, n is a positive integer, c is the speed of sound (1,125 ft/s), and L is the room dimension. A room that is 10 feet wide has its first axial mode at 56.25 Hz — the bass at 56 Hz will be very loud at certain positions and nearly silent at others.
The practical consequence for home mixing is that what you hear at your listening position may not be representative of what is actually in the recording. Bass-heavy mixes often sound thin on other speakers; bass-light mixes sound boomy elsewhere.
Bass traps in corners reduce the energy of standing waves. Room measurement software (Room EQ Wizard is free) can identify specific problem frequencies and guide treatment. For mixing, checking your low end on multiple speaker systems and headphones is essential.