Domain is a pretty ubiquitous word, covering everything from x-values in graphing to internet urls to political borders. They all go back to the Middle English word demain, which meant "to rule". This makes sense for the political borders if you consider that they were all in the king's domain, it makes sense if you think of private ownership for the urls, and it doesn't make any sense for the math-related definitions (and there are like three). Demain comes from a word in French which consistently meant "estate", but inconsistently was spelled demaine, demeine, demeigne, and domaine. The "property" sense wins out as the word is traced further back to Latin dominium, which meant "right of ownership". The word then shifted more to the "owner" as dominium is a conjugation of dominus, which is not an evil dinosaur but a word meaning "lord" (AD is an abbreviation for anno domini, "the year of our lord", though CE is a better, secular way of saying that). Dominus has two potential origins: either through Proto-Italic to Proto-Indo-European demh ("subdue", since lords subdue their serfs) or through Latin domus to Proto-Indo-European dem ("house", since a lord is master of his house).
Adam Aleksic, a leading contender for valedictorian of his high school, is a 210-month-old boy with disturbing interests in etymology, vexillology, geography, and law. Adam would like to one day visit Tajikistan and probably isn't spying for the Kyrgyz government.
The Etymology Nerd