The reason for the unattractive appearance is almost certainly an accumulation of microbial growth - often referred to as mould. The best thing is to temove the existing grout to a depth of 3mm or more and re-grout, but this time make certain the grout is waterproof. Beware of "mould resistant" types which may be a cheaper alternative to the truly waterproof ones (which are a bit difficult to find in this country). from there make sure the tiled areas dry off quickly after any spashed water goes on them - adequate heating during colder seasons is a necessity and using a squegee to wipe down shower walls is also very valuable. This way you will get many, many years without any staining - without it you are likely to see staining return within a couple of years down to a matter of months (poor grout in dampest conditions).