What on earth is a demonstrative deteminer!? Don't worry, it's not nearly as scary as it sounds! Demonstrative determiners (which are sometimes inaccurately called demonstrative adjectives) are just the words this, that, these , and those.
This and that are both singular, meaning they only talk about one thing. This is for a thing that is close to us, and that is for a thing that is far away. These and those are both plural, used to talk about many things. These is for things that are close to us, and those is for things that are far away.
This, that, these, and those are all demonstratives: they demonstrate where things are and how many there are. In the examples above, they all come before nouns, which makes them determiners. But these same four words can also be used without nouns, acting as pronouns. In that case they are called demonstrative pronouns.
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