The April 26 Special Election will be to fill the seat once held by D.C. Council Chair Kwame Brown. It's an At-Large seat.
Four of the D.C. Council's 13 members are elected At-Large, which means that they're chosen by everyone in the city. Two of the At-Large seats are set aside for minority parties. Currently, Michael A. Brown and David Catania occupy those seats (they're both registered Independents). Brown, as council chair, occupies the third of the At-Large seats, while Brown's old seat is currently held by Sekou Biddle, who was selected to fill the seat until the Special Election. (More of that in the "Process" section.)
Whomever wins on April 26 won't hold the seat for a full term -- only what was left of Brown's original term. So, on top of campaigning now, they'll have to campaign again next year. And with the District's primaries likely getting moved up to the first half of 2012, they're really only going to have a few months to settle in and start working before challengers start emerging from the woodwork.