The shuttle exploded because (82 seconds after launch) a piece of foam from the external tank hit the left wing, breaking the heat-shield. On re-entry the shuttle could be traveling faster than mach 25 (about 25 times the speed of sound or 19,031 mph). During re-entry, it could be 3,000 °F. With that speed and heat, a wing could easily be shredded with no heat shield. With the wing the space shuttle lost control, and broke apart in midair.
The crew was David Brown, Rick Husband, Laurel Clark, Kalpana Chawla, Michael Anderson, William McCool