A determiner is a word coming before a noun or a noun phrase to tell you “which one” you are talking about. Determiners include:
articles: a, an, the
demonstrative pronouns: that, this, these, those, etc.
possessive pronouns: my, his, her, its, your, their, our, etc.
possessive phrases: Tom’s, the boss’s, that guy in the car’s, etc. (Note that possessive phrases contain noun phrases, which can then also contain determiners.)
Sometimes determiners are called specifiers. It depends on which textbook and which instructor you’ve got for linguistics.