A noun is commonly defined as a word that is a person, place, or thing. This is a somewhere inaccurate description, as actions (e.g. "running" in "He liked running") and ideas (e.g. "love") can also be considered nouns. Therefore the best syntactic definition of a noun is the rather circular "a noun is a word that goes where nouns go."
A noun therefore is likely to follow a determiner, function as a verbal argument, and to take nominal morphology such as plural inflection. It can be modified by adjectives.
Proper nouns and referentiality[]
Proper nouns (AKA names - written with capitals in English) are special nouns that refer to a unique, salient individual (in the field of semantics). For instance, in a group of women, "the woman" is not referential, nor is "she," while "Mary" is; if we say "give Mary the book," it is clear to who the sequence [meiri] refers.
However, in some instances, a proper noun is not adequate for referential purposes - e.g., if there are two people named Mary in the room, one must specify: "Give the book to short Mary," or "to the Mary over there." Otherwise proper nouns and referential expressions generally do not occur with determiners.
The noun in syntax[]
A noun phrase is a syntactic unit whose head is a noun.
Noun phrases often further include adjective phrases (and therefore adjectives) and other nouns (in compound nouns, such as ice cream truck). Theories of syntax that include morphology as part of syntax also break the noun down further into its various morphemes.
In English, noun phrases are best thought of as subordinate to their determiner phrase; therefore, while the NP is often thought of as the verbal argument, it is actually more accurate to say that this is the DP.