A domain is 'rich', relative to our own intelligence, to the extent that (1) its search space is too large and irregular for all of the best strategies to be searched by our own intelligence, and (2) the known mechanics of the domain do not permit us to easily place absolute bounds against some event occurring or some goal of interest being strategically obtainable.
For the pragmatic implications, see Cognitive uncontainability and Almost all real-world domains are rich.