Why the concave mirror is used …

Concave mirrors are used in solar furnaces, because concave mirrors are the only type of mirror that reflects light in toward a single focal point.  A flat mirror does not have a focal point.  It does regular reflection off all of its points.  A convex mirror does have a focal point, but it is an imaginary point that exists behind the mirrored surface.  The light will reflect up and away from the focal point of a convex mirror.  The concave mirror takes all light that strikes its surface and reflects it all "down and in" toward the focal point.  The collected light at the focal point is very powerful.  It is bright and carries a lot of thermal energy, which is the goal of a solar furnace.  It's basically the equivalent of taking a magnifying glass to burn ants with.  The difference is that the magnifying glass is a lens instead of a mirror, but both devices collect light and gather it into a single point.