The Player's off-hand is a feature introduced in Version 0.1.10. It allows for certain items to be held in the Player's right hand while simultaneously holding another item in the dominant/main hand.
Items held in the off-hand can be used by pressing and/or holding the RMB (Right mouse button, AKA Right Click). So far, the only items that the Juiceling can hold in their off-hand are Grimoires and the Grappling Plunger, but there may be more items that the off-hand will have the ability to hold in the future.