Account number as a unique ID for each account.
Each Account have an ID in database, that can be use, or a complete new number.
Forman and Son Enterprises -> account# 235
Forman Design and Something -> account #244
So when the customer call with questions about the account all you need is the account number (which by the way can also be the phone number) and make it easier and faster to search.
In US a lot of companies associate your phone number with the account number, so when you call, before they answer your call they pull up your account info to speed up the process.