"Non empty", better written as "non-empty" with the hyphen, is used as an adjective in certain cases, generally when it precedes a noun. "That is a non-empty set." If it's a predicate adjective, you'd use "not empty". "That room is not empty." You normally use "not empty" in this way, and not as "this is a not empty room"

As for "why," I can't give you a good answer. It is possible to manufacture compound words in English by using prefixes like "non-" and "un-" and they always will be understood, but some of them are real words and some are not. Play it safe by avoiding them unless you have seen them used, or unless you have checked a dictionary. Usually the meaning of a combination is exactly what you would expect. An interesting exception involves the story of the word "flammable," easily ignited. Originally "flammable" was not a word. The correct word was "inflammable." One of the (rare) meanings of "inflame" is "to catch fire." Unfortunately the "in-" prefix can also mean "non-" or "un-". People saw the word "inflammable" and misunderstood it to mean "fireproof" instead of "dangerous." So safety organizations decided to coin the word "flammable" and use it on warnings.

"Not empty" is ordinary English. The compound word "non-empty" or "nonempty," with or without a hyphen, is a technical term used in mathematics and computer science. It is never used in ordinary English. "This function returns the tuples in the first specified set that are non-empty when evaluated across the tuples in the second set." (If someone said "My glass is non-empty" I would assume she was a math major or computer programmer making a nerdy joke).

"not empty" is correct. I don't really know why but "non empty" seems strange:P