"Shift and tilt" actually comes from the world of view camera photography. Lets say you photograph a building with the base of the camera parallel to the ground. You don't want to tilt the camera up because that might cause the verticals to diverge. With a view camera, you can move the lens up while the film of sensor stays where it is. This allows you to get the top of the building into the scene while keeping the verticals parallel. You can also tilt the front lens board of the camera. When you tilt the lens you also tilt the plane of focus. Imagine photographing a brick driveway leading up to a house. Your client is the brick maker and you want all of the bricks to be sharp right from the front of the camera to way off in the distance. To do this, you tilt the lens in the direction of the bricks.
The irony is that this technique was originally used to make things sharper. Recently it has become fashionable to either use a large camera to simulate a small simple camera or to isolate the area of greatest interest by throwing extraneous elements out of focus. To do this you just tilt the lens back until only a few bricks in the driveway are in focus.
The tilt is also know as the Schiemphlug (SP?) effect after its inventor.
In essence, blurry has become the new sharp.