What is a topological domain?
TADs were initially discovered by computing contact probabilities between regions of the genome using HiC (a chromosome conformation capture method, that try to provide an idea on how the genome is organized inside the nucleus by computing the probability of each contact to be located nearby another locus). People have found that instead of being random, some loci were in contact with some regions of the genome rather than the others, implying some form of functional significance.

In short: a TAD is a genomic region of increased contact probability. They are of functional relevance (for instance, Enhance-Promoter gene expression regulation occurs primarily within one TAD rather than between two (adjacent TADs).

You might be interested in the following papers: 


A 3D Map of the Human Genome at Kilobase Resolution Reveals Principles of Chromatin Looping (might be behind paywall)
Topological Domains in Mammalian Genomes Identified by Analysis of Chromatin Interactions 


Finally, the following picture (extracted from the latter publication) provides an example of two TADS: 



The bottom panel shows the contact probability: two regions of the genome appear to be isolated whereas they are nearby. They show significant self-interaction. One interpretation for that (top panel) is to imagine that the genome exhibit some reproducible condensation, explaining the increased contacts.