This is a remarkably simple tip, but it can really help keep your tile and grout cleaner longer.  Use plenty of water, flush out the mop often, and change the bucket frequently to prevent the water from getting dark.  Dirty mop water acts as a grout stain. and it tends to soak in a little, each and every time the floor is mopped, making it slightly darker each time. That is why dirty grout typically looks dark everywhere except about 1-2 inches from the edge of the room. It is not because people walk everywhere except the 1-2 inches which are closest to the wall. When the floor is mopped, the 1-2 inches (of grout) next to the wall do not typically get as wet from the mop water, and therefore do not get as dark.