The Rift is a world that connects pawns to a multitude of different Arisen. You can easily gain access to the rift through rift stones which act as a portal to the pawn's world. In the rift you will have the ability to search and rent pawns from your friends and or any pawn thats has been upload to the network. Be it a pawn that was customized to soak up damage or a pawn that has a vasse knowledge of the world, while in the rift you have the ability to choose from a large variety of pawns using the refined search options. The currency to borrow these pawns are called Rift Crystals, you gain them by killing certain boss monsters and they can be awarded to you when main pawn returns from another Arisen.
The borrowing of pawns in Dragon Dogma is meant to keep the game feeling fresh and different everytime you play. Typical RPG's tend to force you to pick your main party from the list of story based party members you have to choose from. While the pawn system actually is telling the players to mix it up since the pawns will evolve more and more as they are used by different players.