Are you familiar with the "Cricut"? The Cricut is a vinyl cutter that has been dumbed down for the masses. The problem is that what it makes up for in ease of use, it loses in ability to use custom designs. Anyway, I just mention it because a lot of people have see the Cricut and it helps explain what a vinyl cutter is.
A vinyl cutter is like a printer only instead of the head shooting out ink, it has a blade on the head that cuts the material beneath it. Car decals are typically cut out with a vinyl cutter. You can also purchase a thermal material that cuts out like the vinyl, but can be heat applied to material like tees and totes and anything made of cloth material.
On the software side, you have to create your design as a vector graphic file. Adobe Illustrator and CorelDraw are vector graphic programs. The nice thing about vector images is that they can be scaled to any size without losing quality.
Anyway...hope I've helped explain the vinyl world. It's becoming a great medium for short-run t-shirt designs that a lot of shirt shops are now using.