(mathematics) the set of values of the independent variable for which a function is defined
"In calculus class, we spent most of our time determining the domain of rational functions to ensure we didn't divide by zero."
the content of a particular field of knowledge
"The professor spent the lecture explaining that his research domain covers everything from quantum mechanics to particle physics."
A geographic area owned or controlled by a single person or organization.
"The new mining company quickly established its domain over the rugged mountain range, excluding all local residents from the land."
In plain English: A domain is a specific area of knowledge, interest, or control where someone has authority or expertise.
"His expertise in computer science is respected throughout the entire domain."
Usage: Use "domain" to refer to a specific territory under someone's control or a specialized field of knowledge, such as an expert's domain of study. Avoid using it for general locations unless emphasizing ownership or jurisdiction over that area.
The word "domain" comes from the Latin dominium, meaning property or right of ownership, which entered English via Old French as a term for power. It traveled into Middle English as demayne before evolving to its current sense of an area under someone's control.