That's a chain tensioner.

Single-speed bikes (more like, bikes that don't use derailleurs) often use rear dropouts with a horizontal slot for mounting the wheel. You'd adjust the wheel fore or aft to put the right amount of tension on the chain.

A bike with vertical dropouts needs some sort of adjustment for chain tension. A few have an eccentric bottom bracket that can actually move the crank forward & back. In this case, it's an add-on pulley.