Maimonides refers to washing with sand.
He may wash his clothes in water, but not with soap or using sand.
Does anyone know how this was done?
Sand is an "abrasive". As such, it is good for dislodging/removing dirt, etc. trapped in clothes.
But after you do this, you have to wash out the sand.
Soap does a similar job in a different way (using "chemical," rather than "mechanical" means).
Pretty much the way it sounds. (oddly, I had to wash my hair with sand this week, so I can report that it works pretty well.)
Washing with sand is still done today. Soap is generally thought of as "chemical" removal of dirt and oils, while sand is "physical" removal of dirt and oils.
Because sand is fine, coarse, and usually not too absorbent, it will rinse right off. There are many common products today that work the same way. Lava brand soap is a good example.
Sand is also often used in cleaning cookware. For example, when camping, you can use sand to clean a cast iron fry pan. You can not use soap, and salt may be too damaging to the environment (in a large concentration).
Washing with sand, (and not water or soap) is a good way to "clean up" when water is scarce. It will remove dirt and oils, help with sweat, and generally leave you cleaner than using nothing at all.
That said, you're reading a religious document, so there is certainly a religious reason behind using only water. Unfortunately, I don't know enough to really answer the why.
Only that washing with sand and water, or only sand, are both viable and in-use today, though perhaps soap and water (or only "soap" if we include disinfectants) is more common.
I'll give you an anecdote. When I was a kid, I grew up in a third world country. We used to wash our bodies with sand. It actually worked great, and was better than soap. Basically, you pick up a handful of sand, and rub it against yourself in the shower or near the ocean. It removes all dead skin, oil, and impurities.
I would imagine clothes would wash really well, simply wetting them, and rubbing the fabric together with a little sand. But I is probably abrasive, and I imagine it would damage the fibers if they were too fine.
The same way you wash pure wool by hand basically, if you don't use dry cleaning. Wetting the fabric, introducing a little sand, and rubbing the fabric together, keeping the fabric wet.
Heck, I've used sand on many occasions, both with and without soap....but always with water. As other folks here are saying, sand is amazing, depending on what the task is and also your circumstance.
When i was in Newfoundland, Canada, as a youth, i was out fishing in very remote areas for four weeks, with my uncle. We used sand, along with mild soap and water, to do dishes at campsites. It worked great.
I also used sand, now and then, as a shampoo substitute....and I was amazed at how well it cleansed my oily teen hair and in fact made it shimmer !
We used sand and pebbles to assist in doing tough, grubby laundry, too, and unfailingly it worked quite well.