If you aren't familiar with the kind of beauty you can achieve with foam art, you're likely to look at a term like "hot wire foam cutter" and think that it's a kind of industrial tool. On the contrary, it's a tool that's used by thousands of skilled craftspersons all over the world. There are even foam art galleries that display foam sculpture.
The hot wire foam cutter is the basic tool that you use in foam craft. It's a simple enough device that you could actually build one right at home. You can probably guess how it works. The device holds a wire that is electrically heated. When you pass this wire (that heats to 200°C) through a sheet of styrofoam, it just vaporizes the immediate area of foam that it is in contact with.
Now the traditional hot wire foam cutter design used to be a large and fixed one. It was a tabletop model, and you would guide your foam material through it. This is usually not a good idea for artists though. It might be a good idea for industrial purposes where large sheets need to be cut into four manageable sizes. For the home foam craft enthusiast though, a small handheld hot wire foam cutter can be ideal.
These are quite inexpensive well-regarded brands such as Woodland Scenics sell some pretty capable handheld units for as little as $30. A handheld unit such as this can work great for free-form foam sculpting. You just hold it like a rather large pen, and carve whatever shape you want into a block of foam. If you're working on your own props for a Halloween party for instance, you could make some pretty hysterical relief signage, ghouls and tombstones this way.
The hot wire foam cutter is the only tool to use for foam art. You might think that you could get away with using a knife. Couldn't a really sharp knife do the same job? Perish the thought.
Not only can a knife never be as sharp as you want it to be or even maintain its sharpness, you just can't wield it with the kind of control you need to really make shapes.
You will find plenty of DIY information on the Internet for how to make hot wire foam cutters yourself. You should probably buy your first ready-made. You need to get a feel for how these things are supposed to work before you make something on your own.