Suppose you write a class SavingsAccount to represent savings accounts at a bank. Each object represents a particular customer's account, and has data members storing the customer's name and the account's current balance. The class also has a member function to increase an account's balance by the interest earned in one day.
In such a class, how would you represent the daily interest rate? The interest rate may change, so it has to be a variable instead of a constant. You could make it a member of the class, but then each object would have its own copy. This is not only a waste of space, but it also requires you to update every single object each time the interest rate changes, which is inefficient and could lead to inconsistencies.
You could make the interest rate a global variable, but then every function would be able to modify its value. What you want is a kind of global variable for an individual class. For such situations, C++ lets you declare a member of a class to be static.