In TeX speak, every "box" -- think of a rectangle, except that the rectangle could have one or more of its "dimensions" set equal to zero -- has height, depth, and width. The width part has the obvious meaning, being measured along the horizontal axis. The height of a box is measured up from the baseline, and its depth is measured down from the baseline. (One could refer to the sum of the height and depth of a box as its "total" height.) For typesetting purposes, it's essential to know both the height and depth of a box because when TeX creates a line of text out of a series of boxes, the boxes need to be aligned on the baseline.
Two quick examples. The box that contains the lowercase letter x
has positive height and width but zero depth because the letter doesn't reach below the baseline. The lowercase letter j
, in contrast, would be encased by a box that has positive height, width, and depth because it has a descender (a component that reaches below the baseline).
The strut
you bring up in your question is a special TeX box which has the height and depth of the parenthesis symbol -- (
-- but has zero width and is therefore invisible. Being able to insert such a special box is a very handy typographic tool, because it forces the box that encloses it and the other ("real") items in the group of boxes to have at least the height and depth of a parenthesis.
The following code demonstrates how inserting struts can make the output look more polished. (The formula I've come up with is obviously highly contrived!)
In the first version of the formula, all three surds (the square-root symbols) have different depths and heights. The formula's appearance isn't exactly dreadful, but there's a distracting element: whereas the q
, x
, and k
symbols are nicely aligned along the baseline, the three surds provide a second "line of sight" that rises at a slight diagonal from left to right.
In the second formula, inserting a \mathstrut
-- TeX's \mathstrut
generates a "box" that has the same height and depth as a parenthesis and has zero width -- inside the arguments of the three \sqrt
macros makes the surds all have the same height and depth. As a result, the "line of sight" created by the three surds is now also perfectly horizontal.
Hopefully, then, the insertion of the struts will make for a more polished and thereby more visually pleasing appearance of the overall formula.
\documentclass{article}
\begin{document}
\noindent
A simple formula without struts \ldots
\[\sqrt{q} = \sqrt{x} + \sqrt{k}\]
\ldots\ and with struts.
\[\sqrt{\mathstrut q} = \sqrt{\mathstrut a} + \sqrt{\mathstrut k}\]
\end{document}

height
and (possibly) drops below it bydepth
. For instance, thep
has a depth. Thewidth
is just the width of the text. For documentation on\vbox
\hbox
etc. you can have a look at TeX by Topic.TeX by Topic
is a good starting point. Also, for in-depth explanation I'd recommendThe TeXbook
. For a simple explanation on struts and text height, checkThe Not So Short Introduction to LaTeX
, especially pages 49 and 133-136.\vbox
and\hbox
, as this topic isn't very closely related to that of the dimensions of a TeX box.