algebra precalculus - Two Questions Regarding Polynomial Functions.

I am studying Polynomial functions and their Graphs.

I am currently looking at the definition for a polynomial function and I am trying to arrive at a deeper understanding; thus, please excuse questions that seem obvious.

Nonetheless,

A polynomial function of degree $n$ (What is $n$, a arbitrary variable chosen?) is a function of the form:

$$

P(x) = a_n x^n + a_{n - 1} x^{n - 1} + \ldots + a_1 x + a_0
$$

where $n$ is a nonnegative integer and $a_n$ does not equal 0.

The numbers $a_0$, $a_1$, $a_2$, $\ldots$, $a_n$ are called the coefficients of the polynomial.

The number $a_0$ is the constant coefficient or constant term.

The number $a_n$, the coefficient of the highest power, is the leading coefficient, and the term $a_n x^n$ is the leading term.

Questions:

1) What do the subscripts indicate, such as $n$?

2) In algebra, I learned that constants are for example $1, 2, 3, 4$; however, they describe constants as constant coefficients in the book. Can someone explain the reason behind that?

As you can see, I am new to learning mathematics, so please be simple.