If you have moved into a home or business with Tile and Grout, or had it installed recently you more than likely were never told how to properly maintain it. You also may not be aware that most grouts installed require a sealer to be applied, to prevent the staining and discoloration causing you problems right now. Every time you mop on your unsealed grout, as soon as the mop water gets even a little dark you are actually staining the porous material. To remedy this you would need to A. Mop only with a PH Neutral floor product that is not going to leave residues behind and B. Dump your mop water or avoid mop buckets for weekly cleanings and resolve to only using the mop bucket when a deep clean is required every 3-6 months or depending on your soil level, traffic, pets, region, etc. As soon as foods or other contaminants come in contact with the porous grout, those occurrences can also cause stains to form, which mopping will only further push down into the material. Once a year having a professional Tile and Stone Restoration Company in for a cleaning is highly recommended, during these cleanings extraction units are used to rid the grout of bacteria and soil unless of course a permanent sealer has been applied then you would just be maintaining the integrity of the sealer.