The Compass puts a red arrow on the HUD that will always point to the level exit, even when it's off-screen.
The compass is usually somewhat helpful as it allows you to plan your route through the level more efficiently, allowing you to run to the exit quickly to escape the Ghost or take a shortcut to avoid enemies.
It is perhaps most valuable in the Ice Caves, where it can often be the difference between life and death.
By showing where the exit is, it will help you to avoid ending up on the wrong side of the bottom of the map, which can be frustrating and often difficult to rectify, especially if you don't have many ropes.
Along with the spike shoes and the jetpack or cape, it is probably the most important item to have in this area.