Molded expanded polystyrene, or MEPS, more commonly known as Styrofoam, is the same material used to make disposable coffee cups and ice chests. Beads of MEPS are compressed together into sheets of insulation and covered with a vapor barrier. The vapor barrier prevents condensation between the beads. Another type of insulation panel is made from extruded expanded polystyrene, or XEPS. This uses a liquified Styrofoam to make the panels and doesn't need the vapor barrier, since there are no spaces between beads for condensation to form.
Condensation occurs in walls when cold outside air meets the warm interior wall. Water condenses in the walls, and this can lead to rusting wires and pipes, the growth of mold and mildew, and the rotting of wooden studs. The severity of the problem depends on the humidity in the atmosphere. A vapor wrap around the house can help prevent condensation, but condensation can still be a problem.
Installing foam insulation panels on the outside of your home eliminates condensation within walls because it prevents cold outside air from getting to the warm interior wall. Without this temperature difference, water doesn't condense. In hot climates, foam insulation panels prevent warm, moist outside air from coming into contact with cooler interior walls, again preventing condensation within the walls.
To prevent condensation, you must seal all joints and gaps where the foam insulation panels come together, turn corners, etc. You also need a good roof overhang to prevent water from running down behind the insulation panels. If you've never installed this kind of insulation before, you may want to consult a professional.