As a wheel-chair bound MSer, I have found microfiber rags to be energy- as well as money-saving. See more…

Instead, I do what I can and depend on family and friends. And one of the best things I use lately is microfiber rags.
What is it
Microfiber is a synthetic, usually made from polyesters. It is called microfiber because it is so fine, Wikipedia says it is even finer than silk thread, which has a diameter itself 1/5 the size of a human hair.
The combinations of teeny, tiny materials bundled into teeny, tiny thread, are then woven into fabric used for upholstery, apparel and cleaning products.
Most often, in cleaning products like these towels, the fiber is notched. The area between the notches creates a larger surface on the fiber itself, the better to attract and cling to dust and other particles, and to absorb liquid.
A non-notched microfiber can exist, but is basically just a soft fabric: it isn’t designed to be absorbent.
Here is a public domain image I found showing the difference between a regular cotton fiber and a microfiber:

Vassia Atanassova – Spiritia • Public domain
Why I use
Traditional cleaning cloths require a cleaning agent (detergents, soaps and other chemical cleaners) to dissolve the dirt, which then needs to be rinsed off, or it simply just moves the dirt around.
But the notched fibers of the microfiber cloths are able to pick up and hold dirt until you are able to safely shake it out or dispose. So the MF can be used with just water, so it doesn’t need to be rinsed. (Read: easier for me)
Now I don’t usually like the feel of synthetics, and I especially don’t like the lack of absorbency of them. But the use of notched microfiber in towels, for example, has made them wildly absorbent.
Turns out, MF towels were first used at swimming pools. They dry quickly, I assume because of the fiber size, and don’t become stale if damp, I assume because of the polyester. Even the small ones will dry a body quickly.
MF is also static-free. But as I’ve already said, this can be problematic when using plush-textured rags in cleaning electronics, like I do.
So while the material is good for this, it may be safer to use flat instead of nappy MF cleaning cloths for TV and computer screens. Or clean them really well between uses.
To clean
Another benefit of MF is that they are washable and reusable, unlike paper towels.
But towels made of microfiber should never be washed with oily, soap-based detergent or subject to fabric softener. The oils and surfactants in these will clog the MF and decrease their ability to absorb.
In fact, some sources recommend that you occasionally just boil them in plain water for 10 minutes. The boiling water will relax the fibers to refresh their ability to absorb.
Related stuff
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Microfiber | Wikipedia
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Microfiber for Green Cleaning | Wellness Mama