The inclined plane is not what people think of when they think "machine," because inclined planes are present in nature. Go look at the slope of a hill, and you are looking at an inclined plane. However, as a mechanical concept, it is one of the most fundamental principles in engineering, and one of the classic "six simple machines."
An inclined plane is any flat surface that ends at a higher point than where it began. This does not necessarily imply that an inclined plane need to be purposely built to qualify--any natural slope is also an inclined plane. It is one of the six simple machines.
An inclined plane gains mechanical advantage by trading the amount of energy required to lift an object for increasing the distance over which it must travel. Walking up a 60-foot hill is easier than climbing directly up a 60-foot cliff would. However, you also travel further than 60 feet in order to do so. Discounting friction, the same amount of energy is expended in both cases, but scaling a cliff requires that energy to be expended in a shorter period of time.
Strictly speaking, no one invented the inclined plane, since the actual object is present in nature and was being used even before the principles behind it were understood. Archimedes, the ancient world's great mechanical scientist and inventor, did not even include the inclined plane in his list of simple machines. However, it was clearly a fundamental engineering tool in the ancient world, even if no one was giving it a place with the screw or the pulley. The idea of the inclined plane as a machine in its own right began to take shape during the Renaissance, and Galileo included it in his work "On Mechanics," but he did not invent it.
Obvious uses of the inclined plane are in chutes, ramps and slides. Less obvious are the use of the inclined plane in blades, which are two inclined planes meeting along a common edge. This works by transferring the resistance in splitting an object to the faces of the inclined planes, driving them apart. This conserves force relative to simply pulling something apart.
Some physicists argue that the wedge, another simple machine, is simply an inclined plane used for another purpose (as described above with how blades work). After all, a wedge or chisel is a splitting tool that is often a single inclined plane used to apply force, rather than to lift, and the mechanical advantage conferred is similar, even if applied for different reasons. However, for the sake of simplicity and tradition, the six simple machines typically address the wedge and the inclined plane separately.