Terms such as n-1 and n+1 tend to appear when there is list of things we wish to refer to, or when we have a process which moves from one state to another, often in response to the flow of time, usually in discrete time periods.
In the situation where we have some property or process which evolves over time, such as the number of cells when something is growing in biology, the total amount of money to be paid under compound interest or the probability of picking a marble of a specific colour from a bag on the current attempt you will find terms such as n-1.
In such cases, to ] calculate the state of the system, we use the last state and some update which tells us how to move from the last state, n-1, to the current state, n.
You could of course view from a slightly different perspective and call the last known state, n, and the current state, n+1.
The distinction between these two naming conventions is reasonably arbitrary, and they essentially resolve to the same meaning.
You might want to start out by thinking of n-1 as representing the previous item in a sequence or list, or the last state of a system or process.