See Wikipedia - Domain Adaptation. Usually in NLP, domain adaptation becomes necessary if the training data is from a different genre than the testing data - you train on newswire, test on medical domain, for example. Since natural language is so varied, often the domains are quite different, with different lexical items, syntactic patterns, and semantics. For a definition of what a domain is, see van der Wees 2015 - What’s in a Domain? Analyzing Genre and Topic Differences in Statistical Machine Translation or references in Gururangan 2020.
See also Awesome Neural Adaptation in NLP or here (old) A curated list of unsupervised domain adaption papers in NLP (not including MT).

Table from Ramponi & Plank 2020.