We develop a cohomological description of explicit descents in terms of generalized Jacobians, generalizing the known description for hyperelliptic curves. Specifically, given an integer n dividing the degree of some reduced, effective and base point free divisor m on a curve C, we show that multiplication by n on the generalized Jacobian Jm factors through an isogeny ϕ : Am --> Jm whose kernel is dual to the Galois module of divisor classes D such that nD is linearly equivalent to some multiple of m. By geometric class field theory, this corresponds to an abelian covering of Ck := C xSpec k Spec(k) of exponent n unramified outside m. We show that the n-coverings of C parameterized by explicit descents are the maximal unramified subcoverings of the k-forms of this ramified covering. We present applications to the computation of Mordell-Weil ranks of nonhyperelliptic curves.