Tg is the temperature range over which a polymer's molecular chains gain enough mobility to move past one another. Below it the polymer is rigid and glassy; above it, soft and rubbery.
For coating formulators it is the single most useful number for predicting film behaviour. A high-Tg polymer at room temperature is hard, block-resistant and scratch-resistant, but brittle. A low-Tg polymer is flexible and tacky, gives good adhesion, but blocks in the reel and marks easily.
In water-based emulsions Tg is closely linked to minimum film-forming temperature. A high-Tg emulsion may not coalesce at ambient conditions at all without a coalescing solvent, which is the standard formulation compromise: use a high-Tg polymer for the film properties, add a coalescent to get it to form a film, accept the VOC contribution.