Since grout is not waterproof and moisture is absorbed into the grout when it is not sealed, moisture is being held in suspension on the grout. As the shower washes skin cells off the body, these cells collect in the grout. The result is the development of mold on the grout lines. Cleaning these grout lines with a bleach based product will remove the mold but will not stop future mold development when the shower is used.
If the grout has not been sealed, the moisture can get past the grout and be absorbed into the backing of the ceramic.
If the house was built from roughly 1965-90, the wall behind the tile is covered with drywall (greenboard). When drywall gets moist, it expands and swells, the grout cracks as a result, more moisture gets in, the tiles loosen, the wall leaks and you need a new shower.
Newer showers have cement board behind the tile instead of drywall. Trade names such as Dura Rock, Wonder Board or Hardi-Backer may be familiar. The cement board does not swell when moist, does not flex or easily puncture like drywall and can be coated with a waterproof covering.
Sealing the grout would have prevented the entire problem.
If the tiles are attached to drywall, the shower walls require a complete tear-out and rebuild.
If all tiles inside the shower are still securely fastened to the cement board (determined by tapping on the tiles with knuckles and observing the intact grout), then it is completely salvageable.
This repair involves removing the caulking, thoroughly cleaning the grout, sealing the grout and replacing the caulking.