The system is called simultaneous polyandry, and it is rare among birds. A female African jacana averages close to twice the mass of a male, holds a territory over floating vegetation, and pairs with several males within it, typically two to four. She lays a clutch in each male's nest and moves on.
The male does everything after that. He incubates the four eggs, and carries chicks tucked under his wings with their legs dangling, moving them away from danger. Female competition for territory is intense, and takeovers occur in which a new female may destroy existing eggs. Meanwhile paternity is not assured: males in a female's territory can be cuckolded, and males adjust their care accordingly in some jacana species.
Why this arrangement arose here is still argued. Abundant floating vegetation supplies a rich, predictable food supply and heavy predation on nests makes replacement clutches valuable, but the decisive factor has not been isolated.