What does \smash do, and where is it documented?

\smash is a macro defined as

\relax \ifmmode \def \next {\mathpalette \mathsm@sh }\else \let \next \makesm@sh \fi \next 

and \mathsm@sh is defined as:

\setbox \z@ \hbox {$\m@th #1{#2}$}\finsm@sh 

and finsm@sh is defined as

ht \z@ \z@ \dp \z@ \z@ \box \z@ 

A simpler version of the command which makes what it does a bit more obvious is this one from TeX by Topic:

\def\smash#1{{\setbox0=\hbox{#1}\dp0=0pt \ht0=0pt \box0\relax}}

which basically takes some content and puts it into a box of 0 height and 0 depth.

It's documented in the TeXbook and also in TeX by Topic, which is included as part of the TeX Live documentation (texdoc texbytopic should bring it up.)

The actual macros in the LaTeX kernel can be found in the document source2e.pdf (also available through texdoc.)

Some packages such as amsmath redefine it. See also

• Which package defines \smash?

This answer attempts to address @BenCrowell's desire for examples of how smash can affect the output. As comments have indicated, it is height and depth, not width, that is affected by \smash. What this affects, therefore, is the vertical space allotted for the text, which could affect vertical placement of pre- and suc-ceding lines, the positions of super and supscripts (associated with the smashed material), as well as material stacked in conjunction with \smashed text.

\documentclass{article}
\usepackage{stackengine}
\begin{document}

\noindent Affects placement of pre-\\
$\displaystyle\frac{Q}{Z}$ (vertical space widened to account)\\
and suc-ceeding material\\
$\displaystyle\smash{\frac{Q}{Z}}$ (vertical space not widened)\\
See what I mean?

\bigskip
Now let's look at super/subscript placement.
\[\left(\frac{a}{b}\right)^a_b\]  
Compare if fraction is smashed:
\[\smash{\left(\frac{a}{b}\right)}^a_b\]  

Now for certain types of stacks:
\Shortstack{a b fg d e} versus \Shortstack{a b \smash{fg} d e}.

\end{document}

For what it's worth, from User’s Guide for the amsmath Package:

The command \smash is used to typeset a subformula with an effective height and depth of zero, which is sometimes useful in adjusting the subformula’s position with respect to adjacent symbols.

With the amsmath package \smash has optional arguments [t] and [b] because occasionally it is advantageous to be able to “smash” only the top or only the bottom of something while retaining the natural depth or height.

For example, when adjacent radical symbols are unevenly sized or positioned because of differences in the height and depth of their contents, \smash can be employed to make them more consistent.

And they provide an example using \smash[b] under the square root symbol:

Without this option:

With it:

\sqrt{x} + \sqrt{\smash[b]{y}} + \sqrt{z}

The second radicand has reduced vertical limits for its bounding box.

This years-old question is still useful. Some comments, presented as an answer:

\smash is not restricted to math mode. It works in ordinary text, and AFAIK in all instances of printed text, even page headers and footnotes.

For example, in an artistic page layout, page headers could smash an image into the gap between header and main text. This has been done.

As already noted, \smash continues to occupy its normal horizontal space. If you smash some text to a distant part of a page (this is possible), then a gap will be left, where the text would ordinarily appear. You could absorb this horizontal space by following the smash with a suitable negative \hspace or something similar. Might make a difference if that happens to occur at a line break. I believe that this is the strategy used by the textpos package.

If you are familiar with image layers in a graphics program, that is similar to what \smash does. By analogy, the smashed text is moved "in the z direction" to a new layer. In HTML, the analogy is absolute positioning with a changed z layer.

I believe that ordinary text, when smashed, does not create a "PDF layer" that would be forbidden in some versions of PDF/X. But I am not certain. In any case, a smashed image would create such a possibly-forbidden layer.