In graph-theoretic mathematics, a cycle double cover is a collection of cycles in an undirected graph that together include each edge of the graph exactly twice. For instance, for any polyhedral graph, the faces of a convex polyhedron that represents the graph provide a double cover of the graph: each edge belongs to exactly two faces."

Source : Wikipedia

Put another way :

In every bridgeless graph one can find a family C of cycles such that each edge appears in exactly two cycles of C."

Source : North-Holland Mathematics Studies, Volume 115, 1985, Pages 1-12

The conjecture was first proposed in 1973 by mathematician George Szekeres. It's also sometimes known as the 'circular embedding conjecture'.

To date, the conjecture has neither been proved nor disproved.