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Prevents the opponent from attacking for 2-5 turns. Either Pokémon may switch at any time, but the user is only permitted to use this attack until the 2-5 turns are up. Ghost Pokémon do not receive any damage, but they are still immobilized. If the target switches, the duration of this attack will be renewed and an additional PP will be used. If the user switches out, the target is still immobilized for the duration of that turn. All the hits will do the same damage as the first hit. If the first hit is a critical hit, all subsequent hits will be critical hits too.
RBY partial trapping moves might be the most obnoxious moves ever. For its duration, the target will be able to switch but it won't be able to attack. It gives the user free switches and it slowly gets your health down until you are in Hyper Beam KO range. It's a move basically used to buy turns and win very, very slowly. You can see Wrap being used mostly by Dragonite on its dreaded AgiliWrap set, which uses the speed of Agility to then trap all opposing Pokemon with Wrap, lowering their health until they are in KO range. The only reliable check to this tactic is to paralyze the Wrap user and, in the case of Dragonite, try KO it before it negates the speed drop with Agility. Another way to go through it is to select an OHKOing move waiting for Wrap to fail. All in all, a very annoying tactic.
Bind is an equivalent move, but with less accuracy.
Fire Spin is a Fire-type equivalent, but with less accuracy.
Clamp is a more powerful Water-type equivalent, but with less accuracy.