One difficulty many hobbyists run into is that Styrofoam tends to be harder to glue than other materials. While plain old Elmer's glue can work, there's a good chance it's not going to work for long. In addition, hot glue guns are out of the question since those will cause the Styrofoam to melt and give off toxic fumes. However, there are specialty Styrofoam adhesives that can be used to make sure that any glued bits of Styrofoam hold long and true.
Styrofoam glue is definitely a very specific type of crafter's glue that can be used for a wide array of hobbies and crafts. Believe it or not, a lot of science goes into the making of this stuff to make sure that the ideal chemical composition is in every bottle or tube, since that's what allows it to stick so firmly to Styrofoam and bond it to anything you need.
This allows for a versatility you don't get with a lot of other epoxies. Not only Styrofoam to other Styrofoam, but also to wood, cardboard, plywood or whatever else you need. So while not the most common type of glue, you can see why it's in high demand to those who need it for specific arts and crafts.
One hobby this comes in useful for is model rockets. Bits of Styrofoam are often used to help hold and maintain the engine in place. If these come loose, then sometimes that rocket is going to crash right into the ground and there goes $30-80 or more.
Another example is for models. Model homes, buildings, bridges, ships, school projects - whatever. All of these can involve the need to glue Styrofoam to make something look right. In this case, skimping to save a few pennies on glue could be a disaster for the project.
There are several companies who produce this stuff, although UHU is probably the best known one among hobby enthusiasts. That said, 3M makes a good Sytrofoam glue, as well as several other companies in the market. There really doesn't seem to be a lot of discussion on whether one brand is superior to any other, but for any arts and crafts project involving Styrofoam, a good Styrofoam glue is a necessity.