What is an 'inversion'?
The average condition of temperature change in the Troposphere is for there to be an overall decrease of temperature with increasing height: a positive lapse rate (see here). However, in the 'real' Troposphere, frequent reversals of this 'normal' lapse are observed, particularly in the lower layers - these zones of increasing temperature with height are inversions (i.e. the inverse of the average state), and are very important for both synoptic/mesoscale meteorology (e.g. fog/stratus formation/dispersal), and pollution dispersion studies, as they cap layers of markedly stable and potentially stagnant air masses.
Examples of inversions include those due to anticyclonic subsidence; cooling land by night (nocturnal inversions); and sea-breeze inversions, where cooler sea air under-cuts warmer land air. Where the inversion is associated with an abrupt lowering of the moisture content (sharp fall of dew point), at the altitude of the temperature rise, then interesting radio-refraction conditions occur, familiar to viewers of terrestrial television in stagnant anticyclonic episodes.