Grout is porous. When you mop, the dirty water runs off the smooth tile and settles in the grout lines, and over time light grout turns gray or brown.
Switching to a clean, damp microfiber mop and changing the water often helps slow it down. Avoid vinegar and harsh acids on a regular basis, since they can etch grout and some natural stone.
Once grout is already dark, surface mopping won't bring it back. It takes a cleaner that breaks down the grease and soil in the pores, scrubbing along each grout line, and then rinsing and extracting the residue so it doesn't dry back into the grout.
Kitchens, bathrooms and entryways usually show the biggest difference. Showers benefit too, where soap scum and hard-water buildup collect in the lines.
If you have cracked or missing grout, it's worth fixing before water gets under the tile. We'll point out any trouble spots during the cleaning. Call Anorve Services at (303) 912-6005 for a free estimate.