The term Reflex in a camera refers to use of a mirror and lens, usually in the viewfinder system. In a reflex finder, the mirror is either behind the taking lens (single-lens reflex - SLR), or a second lens, similar to the taking lens (twin-lens reflex - TLR). This normally involves using the mirror to shift the image away from the film plane to where it can be easily viewed by eye.
The advantage of using a reflex viewfinder is that a better impression of the framing, focus and depth-of-field can be gained. With an SLR, using the taking lens, the framing and depth-of-field can be viewed directly, although most SLRs have a view slightly smaller than the full frame. A disadvantage of some reflex finders is that the image may be laterally reversed, or even upside-down - making following a subject's movements difficult. SLRs with pentaprism finders avoid this problem. Another disadvantage is the added bulk and weight of the mirror system, and either extra lens or mirror movement mechanism, and in an SLR, the delay, noise and vibration caused by moving the mirror.
See also: reflex finder.