a variable comes in 3 types
1) local, can only be 'seen' in the formula
2) global, can only by 'seen' in the current report
3) shared, can be seen in both a subreport and the current report
A variable, is just that, so if you chose a numbervar, there a 'place holder' for your values. The report would need to initialize the variable from somewhere (I am assuming from the database, but it doesn't need to be). As for math, you said an analogy is the bank statement, so at some point it is set to the current balance (usually the initialization is in the group header, but it might be the report). The variable is incremented (usually in details) and in your case the incrementing would be to subtract the value from your variable. Finally the variable is displayed, this might be in details and/or group footer.
Does this help?