How does Stereolithography work?
A CAD file is translated into a surface model made of thousands of triangles (STL)

This file is then sliced into layers (SLI).
The SLI files are loaded into the machine and drive the motion of a UV laser
The laser cures a liquid photopolymer from liquid to solid
Here is a SLA Machine:

Once the first layer is cured, a stage is lowered by .002 to .015 in. depending on the accuracy. Each layer will self-fuse itself onto the others. At the end, the stage rises and the component is lifted out and cured in its entirety, as seen below.

All pictures courtesy of www.howstuffworks.com/stereolith.htm