The title generally bestowed when multiple people head the concom for a science fiction convention, sharing the traditional duties of the chairman. Traditionally, anything that the convention does is the chair's responsibility since responsibility flows upwards.
There are several reasons why a co-chairmanship arrangement might be used:
(1) When there is no one who is fully qualified to chair a convention, the idea of finding two people who each fall short of ideal, but whose strengths are complementary and having them co-chair in the expectation that their weaknesses will cancel and their strengths combine. It usually doesn't work out that way, since it's as common for the individual weaknesses to add up as it is for the individual strengths.
One common problem with co-chairmen is that the committee discovers that if Daddy says "no", I can always ask Mommy: unless the co-chairmen coordinate very closely and have complete trust in each others' decisions, this will work. Since this is quite hard and requires high management skills (and if either of the co-chairmen had those skills, they probably would have been appointed as sole chairman), it is common for co-chairmen to divide up responsibility. This cuts down on the ask Mommy/ask Daddy problem, but risks having a dual convention structure where the two sections don't coordinate very well. And, since the problem that the co-chairmanship was created to solve was that neither co-chairman was really up to working on their own, this usually struggles to achieve mediocrity.
(2) When a group's politics means that there are two competent candidates and neither is willing to let the other chair, a co-chairmanship is sometimes tried. It takes a high degree of maturity on both parts and usually works about as well as can be expected.
(2a) Sometimes the two individuals come from two groups which are running the convention in coalition. This works like #2, above, with the added strain of culture clashes.
In both cases (1) and (2), it's not unusual for one of the co-chairmen to become the dominant decision-maker. In case (1), this is usually unfortunate, but in case (2) where both co-chairmen are competent, it can work well as long as ego-bruising is avoided.
(3) Somewhat more successful is when a con is chaired by someone unsuited to run a convention — frequently when someone runs a bid committee and expects to chair the resulting convention. Appointing a co-chairman (who will actually run things) as a face-saving device can be successful.
(4) Couples can often function successfully as co-chairman as long as their marriage is strong enough, since this eliminates most of the Mommy/Daddy and communications problems.
(5) And sometimes any of these possibilities work out. But don't bet on it.