Silver chests are basically a mini game that you play to give you something extra. Usually if you win the game you get a treasure card and some coins (atleast that's all i've gotten). The point of the game is to make a whole line from one end to the other using the pipes. About the third or fourth time you do it you start to get the hang of it. ;)
The Silver Chest is found mostly in Marleybone and starts the game "Shock a Lock"
The object of the game is to make a continuous pipe that connects the targets on the left and right sides. This is done by arranging the pipes available in the squares.
Generally, you'll want to open up all of the squares and then swap pipes. You can swap pipes by clicking on any two squares; they don't need to be adjacent. The game has a short timer, so you'll need to hurry along.