Grout is that plaster-like substance that seals the floor so water and cleaning solutions can't get in the sides of the tiles or under it to loosen the adhesive. Most grout either matches or is darker than the field tile. Unlike most floor tile, grout can soak up dirt and cleaners and become discoloured. Before you have to dig out the grout between floor tiles and re-grout, though, it's good to know that there are some simple steps you can take to avoid that problem.
The first step should always be prevention. Grout used with floor tile should be sealed, especially if it's light-coloured. Clean and seal grout annually with a manufacturer-recommended grout cleaner and seal with the right sealer. You should be able to wipe up spills and food as easily as on the tile.
Soiled or stained grout can also be cleaned using a grout brush (or hard-bristled toothbrush) and a poultice of baking soda. Make the poultice by adding a little water to baking soda to make a thick paste. Wet the grout and your brush, dip it in the poultice and scrub only the grout between the tile. Wipe clean with a damp cloth or spray a little water on and wipe off the baking soda with a soft rag. If you are cleaning unsealed grout, let this be your warning. Get some grout sealer and seal the whole floor..
On occasion, You'll find a stain that can't be removed by scrubbing alone. You'll need to try a half-and-half solution of bleach and water. Or try one of those bleach pens that are sold for stain removal-they have just about the right sized tip to fit the grout lines. Again, rinse carefully with clear water.
If the stain simply will not come out, your only choice may be to take the grout out and replace it. Before you dig it all out, though, try one of those little hand-held rotary tools or a mini-sander and abrade just enough grout out to remove the stain. If the stain is shallow, seal the surface and you're done. If, however, the stain is deep enough to lower the surface of the grout below the edge of the tile, rough up the grout surface a bit, wet it down and reapply enough grout to raise the level to match the tile. Finish as you would any grouting project.
Know what kind of grout you're using and use the appropriate commercial cleaners. Check with your tile merchant or hardware store guy to make sure you're spending your time and money wisely.
Never use other household cleaners with bleach. The reactions release toxic fumes.