You get a lower interest rate. Banks generally can't require you to have an account there to get a mortgage, however they can give 'discounts' to customers that also have their accounts at the bank. Close your account and you are no longer a customer and lose the discount.

Banks frame it as "it's one of the factors used by our opaque black box algorithm to determine your rate". To find out the exact weight of every factor beforehand, I would have to submit N applications, processing of which is on the order of a week or so.

When I was 'shopping' for a loan (in Sweden) I got an explicit price list. As in "our base rate is X%, if both of you move your main account here we'll offer you Y% and if also you move your home and car insurance to the insurance company we own then we'll offer you Z%"