Originally the em was a unit of measurement roughly equivalent to the width of the capital M in a given typeface at a specific point size. Now the em is usually sized to be equivalent to the point size of a given font. In 12 point type (any style) the em is 12 points. In all 24 point type the em is 24 points. This may or may not equate to the width of the M at that point size. Some sources may equate the em with the width of the lowercase m which traditionally was about the same width of the capital M.
Today a common use of the em, or more specifically the em space, is to create paragraph indents in print and in place of pixels or points in CSS/HTML for web pages. The em (or multiple ems) may be used to create additional space around characters in a line of type when normal spacing is inadequate. When a full em is too much, the thin space is 1/5 to 1/6 of an em. The hair space is thinner than the thin space at approximately 1/10 to 1/16 of an em.
In addition to em space and em dash, the em-quad, also known as the mutton-quad, is another em-based measurement. The em-quad was used with metal type to create space between metal type characters on printing presses. It was a square metal spacer that was 1-em on each side. An em space may sometimes still be referred to as an em-quad although they are not necessarily the same width in today's digital type.