Instant Rent is a "feature" of CityVille which allows you to make your residences available to collect from without having to wait. It exchanges cash for coins in an amount that varies depending on the property you select. You can make an individual housing instantly ready or all housing ready.
By any reasonable analysis, this is one of the worst deals in the game. Many argue that it is really more of a "bug" than a feature since it is very easy to accidentally click on a property and summon the "instant rent" screen which gets in the way of whatever it was they were doing.
The pop-up appears once during each game session. Once you exit out of the pop-up screen, if you accidentally click on a residence that's not ready for collection, it will not appear again.