A laser cutter uses computer numerical control (CNC) to read graphic information from your computer and cut or engrave it into material using a laser beam. The laser optics are usually set up to direct the laser beam from one angle (usually from the top down). It moves along an X and a Y axis.
Video of the laser cutting a box: https://vimeo.com/130159461
Whether the laser cuts or engraves the material depends on the way in which the file is set up—it can run the laser using raster engraving and/or vector cutting.
Raster engraving: Raster images are used for laser engraving (not cutting). Raster engraving creates highly detailed graphic images. The laser head moves back and forth engraving a series of dots to form the image from the digital file (like an old printer). Raster engraving is used for all types of images and visuals (logos, photos, text, etc.). Basically anything that does not involve cutting.
Vector cutting: Vector files are basically line drawings consisting of a continuous path. They would usually be used to cut completely through the material. To vector cut, you need to make sure that lines are no bigger than 0.001 inch heaviness. All lines in a file get registered by the laser and are cut. So make sure that your file does not contain any hidden lines (covered by another shape) or any type of marking.
Files for this can basically be prepared in any program that supports these two types of graphic formats (such as Corel Draw, Adobe Illustrator/Photoshop, SketchUp, Microsoft Paint, 123D Make etc.). In the Maker Lab, we've primarily relied on Corel Draw or 123D Make for laser cutting. For example, Nina Belojevic designed a box for our Early Wearables Kit using Rino, then she exploded that 3D model into 2D parts that could be opened in Corel Draw to laser cut. We've also used Corel Draw to print images or engravings. Recently, we've also started to use 123D Make to laser cut 3D models.
Drawn from Nina Belojevic's DHSI 2015 notes on 2D Modelling for Laser Cutting