Microfiber has quickly become one of the most popular materials in cleaning electronics. When your iPhone gets smudged or your monitor gets dusty, you're likely to reach for the soft, synthetic cloth to make the displays pristine again. While it's seen use in various applications over the last few decades, it's become particularly popular among consumers in the last few years.
Technically speaking, microfiber is any stranded material with a strand weight of less than one denier (a denier is a unit of measurement defined as the number of grams 9,000 meters of a strand of material weighs). In terms of consumer use, microfiber is any woven material made of microfibers (smaller than 1 denier), generally made from 80/20 blend of polyester and polyamide. Natural silk is 1 denier, and it's extremely difficult to find any natural fiber suitable for commercial use smaller than that.
most common form of microfiber for electronics cleaning is a looser weave that uses split strands. A machine splits microfibers radially, creating a series of longitudinal grooves down the strands that become statically charged, pulling in bits of debris like dust. This is extremely useful for cleaning screens, but it's obviously not the sort of material you'd use to bat dust bunnies off of your motherboard.
While microfiber cloths don't necessarily "go bad," they do need some care for long-term use. When your cloth gets too covered in dust to be effective, you can either buy a new one or wash the old. If you want to wash, either wash the the cloth by hand or dedicate an entire load to washing many cloths; they're susceptible to heat and should only be cleaned on normal or gentle cycle. Some users recommend buying light-colored microfiber clothes, so the dirt shows up more prominently and it's easier to know when they need to be washed.
The feel of the material varies from brand to brand and product to product, but generally any microfiber cloth suitable for cleaning a surface will be suitable for cleaning your electronics. Just don't use them to clean inside electronics; that's why we have canned air. Well, that, and because it's fun to turn the can upside-down and pretend you're Mister Freeze.