Your normals are out. Go to edit mode, select all vertices, faces or whatever (A key until all selected), then use the Mesh >> Normals >> Recalculate Outside menu.
Normals are basically that each face has an inside and an outside (e.g, skin is dusty yellow on the outside, but fleshy red on the inside). Sometimes when you model objects, multiple extrudes and moving faces around can end up flipping them over. The black edges show you where those flips happen.