To get this you must be playing in a team race (eg. Sonic, Tails and Knuckles all in one team whilst you control one of the characters).
Simply drive into an item box to obtain any item and then press B to offer it to a teammate. When they take it you will be awarded your achievement.
Upon completing the action correctly, you will notice some text to the right of your vehicle with a golden star writing "Item Box Transfer". You will then see it warp away from your kart. This means it has registered your Item Box Transfer!
I created this video to help:
Hope this helps.