Computer cut (die-cut) vinyl is lettering or decals that are cut-to-shape.
Most people who are looking for adhesive vinyl that is cut to shape actually utilize the reference die-cut lettering or die-cut decals a lot. Die-cutting decals and computer cut decals are similar, in that they are both cut out to shape, but differ completely on how that shape is created.
The easiest way to explain die-cut letters and decals is to visualize yourself baking cookies. You get your dough all laid out and then grab a cookie cutter. Cookie cutters are the pre-made shapes that are used to cut-out each cookie to the same size and shape producing infinite amounts of the same product.
Computer cut vinyl ends up looking exactly like die-cut vinyl but the production process is a bit different. There are no pre-made cookie cutters to punch out the shape of your decal or lettering with computer cut vinyl. To achieve the "no background" look that mimics die-cut vinyl via computer cutting you'll need to know a bit about graphic design practices and programs. For computer cut vinyl or decals you'll need a "vector" file. Vector files allow the computer to read the outlines of text and shapes allowing the computer blade to precisely cut all the components of the decal or lettering to shape. Computer cut vinyl utilizes a special printer that has a built in blade for cutting vinyl to shape when the aforementioned specially formatted files, that tell the computer where to cut, are provided.
After the file is cut-to-shape the extra material around the lettering or decal is pulled away. This process is called "weeding". Weeding the computer cut vinyl leaves only the lettering and decal shape thus creating a multitude of graphics that have no background. The "no background" look is very desirable because the lettering or decal is allowed to stand alone by itself with the applied surface as the background color instead of just being a plain square, rectangular, circle or oval print on white or clear vinyl.