Time Capsules are items in Animal Crossing: New Leaf that are given to the player by villagers as part of a favor; they are stored with the player's letters. The villager will ask the player to bury it; after it is buried, it will disappear until the villager asks for it to be dug up.
If the player digs up the Time Capsule and returns it to the villager, they will open it and give the player an item as a reward. If the player does not return it to the villager, or if they open it, the favor cannot completed and the player's friendship with the villager will decrease. If a villager moves out before their Time Capsule is returned, the will send a letter to the player telling them to open it and keep the item inside.
If the player digs up a Time Capsule in another town, they will re-bury it, saying "[...] it was probably buried by someone who lives in this town. I'll put it back where I found it."
A Time Capsule as it appears in the player's pockets