An orogeny describes a series of forces and events leading to the severe structural deformation of the Earth's crust and uppermost mantle (also known as the lithosphere). So in simple terms, an orogeny is a mountain building event. Occurring at the boundary where continental plates meet (th
ough they can occur where a continental plate overrides an oceanic plate), the response to orogenic forces is basically a "crumpling" of the rock, leading to highly deformed and metamorphosed areas of rock, which extend far underneath the resulting mountain belt, and far beyond the front.
The basic tectonics behind an orogeny is a subduction zone causing two continental plates to collide (or as discussed above it can occur at the meeting between an oceanic and a continental plate). The event can cause a number of tectonic features, including: volcanoes, mountain building, island arcs, back arc basins and of course earthquakes.
A spectacular example of an orogeny is process is the Himalayas. This orogeny has been caused by the Indian plate and the Euro-Asian Plate, but all mountain belts have at some stage been part of an active orogeny.
Once an orogenic event has completed the mountain building stage, the tectonics don't just stop! The mountain chain normally continues to uplift, and at the same time eroded; over millions of years this leads to spectacular views of metamorphic rocks and tectonics.
Links to some fantastic descriptions of orogenies and specific orogenic events:
Image: Carsten Nebel