Ball 'n' Chain is a ball that has spikes on it, and rotates in place from a block. It is invincible, but slowly rotates, and is generally easy to bypass. Bowser uses these as dangerous objects and weapons. Although they are used to prevent the player from succeeding, the player can stand on the brick (which is what the ball is chained to) and will keep from being hurt by the ball. These can be found in Bowser's Castles and fortresses throughout the games it has appeared in.
The object was also found to have a small cameo appearance in the Super Mario World TV series in the episode called "Send in the Clown". While Mario travels through Neon Castle, Mario gets very closed to being hit by a Ball 'n' Chain, which drops from the ceiling, as he tries to get through a lava area.
Ball 'n' Chains appeared in Super Mario 3D Land, where the ball was in purple with yellow spikes, and the chain was yellow. In this game, they aren't connected with shackles, unlike Super Mario World, where they are. The object doesn't spin, but instead move back and forth in a pendulum-like way.
In the second last level of New Super Mario Bros. U, a variation of these are found. Unlike the other variations, these have spikes all around them and can't be passed through, only under.