I've seen it refered to in a couple of (closed) questions like this one.
One comment seemed to indicate it's a World of Warcraft term for a second character; is that correct?
What's the meaning of the term?
Dual-boxing refers to running two clients at the same time (of the same game, usually) and controlling them via a single input (usually heavily macro'd). Multi-boxing is the general term applied to more than a single client at a time.
To "properly" dual-box in World of Warcraft, you need two separate accounts. The comment likening naming a dual-boxing character pair to an alt was misinformed.
Dual-Boxing is not forbidden by World of Warcraft's Terms of Service, though those who do the practice are generally disliked by other players, due to their greater presence and combined power level, and the intrinsic PvP nature of the game.
Usually it indicates one person simultaneously playing two accounts at the same time. Since this requires two computers, it's called dual-boxing.
Here's some more (WoW-specific) info: http://www.wowwiki.com/Multiboxing
Dual boxing is the art of controlling multiple characters in an RPG (usually an MMORPG) simultaneously. The other answers gave some great basic definitions so I'll try and go into detail.
Multiboxing usually works by having one character as the lead, and having the others /follow the main and /assist when casting spells or using abilities. As a result, a multiboxer has unparalleled coordination for focus firing as all the characters fire simultaneously at the same target with the press of a button.
However, there are major drawbacks - a multiboxer has downright horrible mobility and can be easily circle strafed or line-of-sighted (hiding behind walls or pillars) into oblivion. They are also very susceptible to fear mechanics, which cause the characters to be separated and facing different directions, essentially making one or more of the followers sitting ducks. They are also doubly affected by latency. Think of a multiboxer as a big, slow, gigantic cannon made out of glass.
There are two main reasons that people multibox, and I'd like to dispel some prejudices. One reason is for the challenge brought by having to tank, heal, and dps on multiple characters at the same time (usually PvE oriented). Highly skilled multiboxers have 10-boxed or even 25-boxed their own raids, taking on all roles by themselves. Look on YouTube for some of these multibox raiding videos, it's truly astounding the amount of skill, precision and planning involved.
The other main reason is for the satisfaction of blowing up people in battlegrounds (PvP), although PvP multiboxing is definitely not easy. You may be able to one-shot two or three enemies, but if the opposing faction knows any weaknesses of multiboxing the multiboxer could easily be a waste of 5 valuable player slots. For example, my 4 Draenei elemental shaman would sometimes instill fear in enemies by zapping everyone with chain lightning, and they would all hold back causing my team to win the battleground. Other times I get absolutely curb stomped when a blood elf jumps into the middle of my characters and casts AoE silence which gives enough time for the rest of their team to pick off one of my characters, and it all goes downhill from there.