What does it mean by 'time' in a random process?

Question

I understand that

A random process is a series of random variables which is composed of two components:

1. time
2. values

Both time and values can be either discrete and continuous.

I have proper/enough examples in my hand. I just need a 'properly expressible' definition of time without formal notation.

A general answer would be

time is the index of random variables in the series.

this is not easy to imagine/perceive.

So, my question here is, what is the definition of time here?