what does boxplot draw?

?boxplot says

   stats: a matrix, each column contains the extreme of the lower
          whisker, the lower hinge, the median, the upper hinge and the
          extreme of the upper whisker for one group/plot.

and that's accurate: please prefer the primary documentation to notes you 
pick up somewhere on the Web.

For the definition of `hinge' see ?boxplot.stats and the references 
therein.  (The box goes from the lower hinge to the upper hinge.)

   Unfortunately I cannot find in the documentation what determines
   ranges of a 'box' in the box-and-whisker plot.

It's right there on the help pages for boxplot, bxp and boxplot.stats,
with references to the primary published literature.

   It is said in "Simple R" (http://www.math.csi.cuny.edu/Statistics/R/simpleR)
   that they are 1st and 3rd Qus usually.

   I tried to add to boxplot lines with (quantile(x,probs=0.25)), but
   lines do not coincide with edges of boxes.

[...]

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595