Description
Variables are indexed in the following way: the first variable has index 0, the second index 1, and so on, until n1, where n is the number of generators of R, the ring of v. Then, if the coefficient ring is a polynomial ring, those variables are numbered starting at n, and so on.
i1 : R = ZZ/101[a..d,t]
o1 = R
o1 : PolynomialRing

i2 : index a
o2 = 0

i3 : index t
o3 = 4

i4 : A = ZZ[a..d]; B = A[r,s,t]; C = B[x,y,z]
o6 = C
o6 : PolynomialRing

i7 : index x
o7 = 0

i8 : index z
o8 = 2

i9 : index r
o9 = 0

Notice that r is an element of B, and so indices are taken from that ring. If we consider r as an element of C, we get a different answer. Variables of coefficient rings of coefficient rings have an index too.
i10 : index(r*1_C)
o10 = 3

i11 : index(b*1_C)
o11 = 7

The symbol index is also as a key used in GeneralOrderedMonoids to store a table that is used to map generator names to the position of the generator in the list of generators.