Meaning of \quad

The word “quad” is a traditional term in typography. It comes from Italian “quadratone” (big square). In old fashioned metal typography it meant a square piece of metal lower than type height that could be inserted between types for spacing them. In Italian typography it's still called “spazio quadratone”.

It's commonly as wide and high as an uppercase “M”, since this is usually the widest letter in a font and occupies a square area.

The command \quad takes its name from this traditional name; \qquad just means ”two quads”. However in TeX the \quad has no height, but only width.

Some more information:

QUAD is the abbreviation of quadrat. It comes from quadratus in Latin (Merriam-Webster).

\quad and \qquad are macros defined by (La)TeX kernel:

\def\quad{\hskip1em\relax}
\def\qquad{\hskip2em\relax}

For TeXicians, the unit “em” is one of the font dimensions. Say, \fontdimen6 of a font in TeX. It originally means the width of capital letter M in a font (see Wikipedia), but it is not always true in practice.

The font dimensions in TeX and the \fontdimen command is described in “Appendix F: Font Tables” in The TeXbook, and “Appendix F: Font Metric Information” in The METAFONTbook.

You can define a macro equivalent to \quad like this:

\def\myQuad{\hskip\fontdimen6\font}

and of course a \qquad doubles \quad:

\def\myQQuad{\hskip2\fontdimen6\font}

In the Not so Short Intro to LaTex, it says that size of \quad corresponds to the width of the character M of the current font.

That is, \qquad is the space of MM.