Kidnapping (also referred to as Loaning) is a twist allowing one tribe to temporarily "kidnap" a castaway on the opposing tribe to stay with them. Since debuting in Survivor: Skye Islands, it hasn't appeared since.
Occurring in Skye Islands, the winning tribe of a reward/immunity challenge gets the chance to kidnap one opposing tribe member as their reward. The person chosen will miss Tribal Council altogether with their original tribe, however, do return in time for the following challenge. This twist allows cross-tribal alliances to form, as well as revealing information to the other castaways about your tribe.
In a later season, this twist was altered to loaning, where the tribe who won the reward challenge was able to temporarily "loan" a castaway for 3 days. The difference between this and kidnapping is the castaway loaned may be eligible to attend Tribal Council and be voted out if they lose the immunity challenge (or if it's a double tribal council). The castaway loaned will then return to their tribe prior to the next challenge.