SCROG is a way to try and maximize use of light for highest yield, usually in a small(ish) grow.
The basic idea is that any light falling on the ground or walls is wasted. For maximum efficiency, you want all the light you're generating to actually strike plants.
One way to get all the light to hit only plants, is to create a flat carpet-like canopy of plants.
One way to accomplish the carpet-like canopy is with a large number of small plants, usually clones, the so called "sea of green" (SOG) growing technique.
Another way is the SCROG or "screen of green" which mimics the SOG, but uses only one (or a small number) of plants. Instead of a grid of many separate plants, the few number in SCROG are pruned and trained by growing along/through a large mesh screen in order to create an even canopy of tops. So you have one main stem stuck in the ground, but maybe 20 different tops branching off and oriented by the screen.
The biggest advantage of SCROG is that it minimizes the absolute number of plants. That can simplify growing them (for example, fewer plants to water). It also potentially assists legality, since legal grows are usually limited to a certain number of plants, and the criminal penalty for illegal grows is often proportionate to the number of plants grown.