This video has been making the rounds lately, but I haven't seen a lot of accurate descriptions of what exactly is going on in it. The "ant death spiral" is a phenomenon noted seemingly only in army ants, which unlike other kinds of ants do not make permanent nests and are always on the move while they're alive. There are over 200 varieties of army ants, and apparently the type featured in this video are blind, and depend on smells to navigate. Typically they follow the scent-trails of the ants before them in the swarm. The death-spiral is an example of what happens when the swarm as a whole gets misdirected -- and a convenient metaphor illustrating the perils of follow-the-leader behavior in any society.
According to The Ant Room:
Beebe (1921) described a circular mill he witnessed in Guyana. It measured 1200 feet in circumference and had a 2.5 hour circuit time per ant. The mill persisted for two days, "with ever increasing numbers of dead bodies littering the route as exhaustion took its toll, but eventually a few workers straggled from the trail thus breaking the cycle, and the raid marched off into the forest."
The phenomenon was first observed in in insects in 1910 by the scientist W.M. Wheeler in his laboratory, who wrote:
I have never seen a more astonishing exhibition of the limitations of instinct. For nearly two whole days these blind creatures, so dependent on the contact-odor sense of their antennae, kept palpating their uniformly smooth, odoriferous trail and the advancing bodies of the ants immediately preceding them, without perceiving that they were making no progress but only wasting their energies, till the spell was finally broken by some more venturesome members of the colony.
If you're interested, there's another video of ant death spirals in Brazil here.