Grout can become discolored and dirty over time. You might think that applying new grout over the old grout will solve the problem, but new grout will have trouble sticking to the existing grout.
A better solution to make old grout look like new again is to apply a grout stain to the old grout. Grout stain comes in many different colors and can be applied with a brush to mask any discoloration. Simply wipe off any excess and allow it to dry. Watch this video to find out more.