A bank reference or status enquiry is usually a form asking the bank their opinion on if you're good for the rent basically, not that many people use them anymore as credit referencing is usually done instead
The agents will usually send a letter asking if the bank think you are good for the sum of the rent.
Bear in mind the banks charge for this and may take the charge out of your bank account if the agents don't pay it when they send the request, it's usually£10-£15 and can take a couple of weeks to come back