If normal mopping isn't getting them clean, you can try bleaching them. Use half bleach and half water, mop the floor, wait 30 minutes, and then mop with clear water.
Maybe your tiles need to be replaced and you need to get new ones. Or, if you want to risk it, try using bleach to clean your floors. I often use bleach and they restore the color of my tiles, but I heard this might not work for all types of tiles