This is a useful item with multiple functions.

Map: This will display a map of Houen. You can move the pointer with the D-pad and can also press A to zoom in.
Poke-Info: This will display information about your Pokemon stats. These may show how much of a chance your Pokemon has of winning a Pokemon Contest. These can be raised with Poroks (the berries).
Trainer-Dex: This will show information on all of the trainers you have fought.
Hall Of Fame: After defeating the Elite 4, you can see your Pokemon that defeated them in the Hall of Fame.