Hello

Suppose, we are given numbers like

1, 2, 3, 4, 5, 6, 7, 8, ...

We can see that 

2nd term = 1st term + 1

3rd term = 2nd term + 1

4th term = 3rd term + 1

So, difference between any two terms is the same

2 - 1 = 1

3 - 2 = 1

4 - 3 = 1

So, we can say that these numbers

1, 2, 3, 4, 5, 6, 7, 8, ... 

are in AP

nth term means any term

Like 1st term, 2nd term, 3rd term, 4th term... we have nth term

nth term for this series will be n

So, nth term = n

Use of nth term is that, we can put any value of n, like 1, 2, 3, 100, 1000, 999, ... we will get our term

That's why we use it