A credit is a measure of how much you would be willing to lend someone. It comes from the old italian word "credito" which means 'belief' or 'trust'.
It does not mean you have lent anything, it just means you are willing to lend him/her that money if they should need it.
So, basically, credit means "financial trust". I trust you with "this much" money or I am willing to lend you "this much" money.
Once a loan is made based on your credit, only the amount you borrowed becomes the debt. For example:
If you have a credit of $25,000 and borrow $5,000, you then have a 'debt' of $5,000 with $20,000 remaining in credit should you ever need it. The company in your example had reached the limit of its credit and wanted the bank to extend (or make bigger) the credit limit. However, the bank was no longer willing to do so.
Credit cards are also a very good example of how credit and debt work.