When we are talking about banking (and not about things like housing), restrictive covenants are contracts made between creditors and debtors in which the terms of the loan (other than the financial terms) are spelled out.
When a bank makes a loan, it typically means for that loan to be used in a certain way. It has agreed to loan the money based on the idea that the money will be used for that specific purpose. The bank, therefore, wants to make sure that the money is actually used for that purpose. For example, if the bank lends a person money to start a business, it does not want the person to use the money to buy a boat. This would reduce the chances of the bank getting its loan paid back.
Restrictive covenants typically come in two sorts. There are covenants about what the borrower must do (affirmative covenants) and covenants about what the borrower must not do (negative covenants). The borrower might be required to keep certain sorts of records. Alternatively, the bank might require that the borrower refrain from taking out any other loans during the life of the loan in question.
In short, these covenants are meant to specify what borrowers can and cannot do. They are a way for banks to try to lessen the risk involved in making loans.