A desk booking app is the phone version of a desk booking system: an iOS or Android app that lets someone reserve a workspace, check in when they arrive and release it when plans change. The browser tool and the app normally run on the same data, so a desk booked on a laptop shows on the phone and a cancellation made on the phone frees the desk everywhere.
The app matters because desk decisions are rarely made at a desk. People book on the train, swap floors when a meeting moves, or cancel from home. The features that carry that are the mobile ones: an interactive floor plan you can pinch and tap, QR code check-in at the desk itself, and push notifications when a booking is confirmed or about to expire. The underlying practice is still desk booking; the app is simply how most employees touch it.