What micro means
Micro is the SI prefix for one millionth (10⁻⁶). Put µ in front of a unit and it becomes a million times smaller: 1 µs is a millionth of a second, 1 µg a millionth of a gram, and 1 µF a millionth of a farad. It sits between milli (m, a thousandth) and nano (n, a billionth).
In medicine, micrograms are often written mcg instead of µg, because a handwritten µ can be misread as m, and a dose a thousand times too large is dangerous. Outside units, μ is also the Greek letter mu: the population mean in statistics and the coefficient of friction in physics.
Micro sign µ vs Greek mu μ
Two characters look the same. The micro sign µ (U+00B5) was part of old Western character sets like Latin-1, which is why it has keyboard shortcuts. The Greek small letter mu μ (U+03BC) is the real Greek letter. Unicode treats them as compatibility equivalents, and normalization (NFKC) turns µ into μ, so many systems handle them as the same letter.
In practice both are accepted for units. Use whichever your keyboard gives you, but stay consistent within one document, because a search for "μg" may not find "µg" in some programs. The one-character units such as ㎍ and ㎲ come from East Asian fonts and are best avoided in English text.
How to type the micro symbol
Mac: Option + M types µ. Windows: hold Alt and type 0181 on the number pad, or Alt + 230. Word: type 00B5 (micro sign) or 03BC (mu) and press Alt + X.
HTML: µ or μ. LaTeX: \mu in math mode, or \si{\micro\gram} with the siunitx package for properly typeset units.
On iPhone and Android, add a Greek keyboard or copy µ from this page. For the length unit, see the micrometer symbol page; for the whole alphabet, see Greek letters.