There are two definitions. The most common one (and the one that any contractor will be familiar with) is simply a remote distribution panel. Or to be even more basic, a commercial-grade power strip. Essentially it's a device that plugs into one power source (frequently a distribution panel, or even an incoming line, but depending on the model it can also connect to a heavy-duty outlet designed to deliver more current) and gives you lots of other outlets at some remote location.
 
The second definition is the one that has special meaning to laserists, and any other tradesman that might need a source of 220 V power when there are only 110V circuits available. In this case, a spiderbox is a device that bridges two or more 110V circuits in order to create a 220 V outlet. Ordinarily I'd link you to the LaserFX.com website where they have details on how to build one, but the site appears to be off-line at the moment.
 
Here's the 
google cache of the page, but without the pictures it's not very helpful.
 
No. To do that all you need is a transformer with a center tap on the secondary that you can connect to one leg of the 3 phase power. The transformer will reduce the voltage to 220 V and also provide you with the neutral conductor for 110. This is very common, as the power that comes from the power plant is 3 phase, and is only converted to single phase (and also stepped down in voltage) when it enters your neighborhood.
 
Most of the time, laserists are more interested in trying to convert single phase 220V power back to 3 phase power to run larger ion lasers. And in order to do that, you either need a rotary phase converter (essentially a 3 phase motor with single phase power connected to one of the pole windings, and a clever set of inductors and capacitors connected to the other two poles to allow it to start), or a motor-generator (literally a single phase motor and a 3 phase generator that share a common shaft).
 
Adam