What is a leaf shutter?

Typically cameras feature a pair of shutter curtains that sit just in front of the sensor and follow each other across the frame: one retracts to expose the sensor, then the other follows to hide it again. This mechanism controls the time of an exposure, letting light hit the sensor for a precise shutter speed. 

One downside of this type of shutter is that at higher shutter speeds (say over 1/200th sec), some part of either curtain is covering the sensor at all times during the exposure. This is because the first curtain has not reached the other side before the second curtain starts it's journey. When shooting with flash lighting this results in black bars over the recorded image, as the shutter was in the way of the light when the flash pulse went off.

In many medium format cameras there is an alternative: the leaf shutter. 
Like a second set of aperture blades in the body of the lens, a leaf shutter opens and closes in an iris formation to control the exposure of light on the sensor. While more complex mechanically, this overcomes the problem of the shutter curtain getting in the way of flash, with many medium format lenses offering the ability to synchronise with flash at much faster speeds. This gives the photographer more flexibility to control the ambient light by stopping down the shutter speed, without sacrificing the aesthetic choice of a chosen aperture and lighting setup.