Determiners are words placed in front of a noun to make it clear what the noun refers to.
The word people by itself is a general reference to some group of human beings. If someone says these people, we know which group they are talking about, and if they say a lot of people we know how big the group is.
These and a lot of are determiners in these sentences.
Classes of Determiners
There are several classes of determiners:
Definite and Indefinite articles the, a, an
Demonstratives this, that, these, those
Possessives my, your, his, her, its, our, their
Quantifiers a few, a little, much, many, a lot of, most, some, any, enough, etc.
Numbers one, ten, thirty, etc.
Distributives all, both, half, either, neither, each, every
Difference words other, another
Question words Which, what, whose
Defining words which, whose
The following words are pre-determiners. They go before determiners, such as articles: such and what, half, rather, quite