The Proximity Effect in audio is defined as an increase in bass or low frequency response when a sound source is close to a directional or cardioid microphone.
In this video Bryan shows you visually what the proximity effect is and how you can use it to your advantage.
If your vocalist or sound source is too close to the microphone it will result in a big, boomy recording. If your vocalist or sound source is too far away, it will result in thin, roomy vocals. The goal is to find the sweet spot where the vocal sits properly in the mix, making the mix engineer's job (in many cases this is YOU) much, much easier.