Tiling is the ability of an effect to manage images that are less than full frame (or in our current nomenclature, less than the full Region of Definition). By tiling the images it renders, a host will render an effect in several passes, say by doing the bottom half, then the top half.
Hosts may tile rendering for a variety of reasons. Usually it is in an attempt to reduce memory demands or to distribute rendering of an effect to several different CPUs or computers.
Effects that in effect only perform per pixel calculations (for example a simple colour gain effect) tile very easily. However in the most general case for effects, tiling may be self defeating, as an effect, in order to render a tile, may need significantly more from its input clips than the tile in question. For example, an effect that performs an 2D transform on its input image, may need to sample all that image even when rendering a very small tile on output, as the input image may have been scaled down so that it only covers a few pixels on output.