Centering tabular: Why does this work?

First of all, your >{{\raggedright}} does nothing, because {\raggedright} is inserted at the start of the cell and the effect is "do nothing", because the declaration is issued in a group. What you need is \arraybackslash (I'll explain why later on).

\begin{tabular}
  {>{\raggedleft}p{\dimexpr.5\linewidth-2\tabcolsep-.5\arrayrulewidth}|
   >{\raggedright\arraybackslash}}p{\dimexpr.5\linewidth-2\tabcolsep-.5\arrayrulewidth}}

You are asking for a two column alignment. Both columns are of type p and the width is

half the current line width, reduced by twice \tabcolsep and half \arrayrulewidth

You have to know that the structure of a row in your tabular is

t C t | t C t

where t denotes a space of width \tabcolsep, C denotes a cell and | denotes the vertical rule, which has width \arrayrulewidth.

Thus, since the width of C is as stated before, the tabular will be as wide as \linewidth:

t + (0.5L - 2t - 0.5a) + t + a + t + (0.5L - 2t - 0.5a) + t = L

(where L is the line width).

Why \arraybackslash? Because \raggedright redefines \\ and so this command could not be used for ending a row. The command \arraybackslash restores the correct meaning of \\. It's not required in the first column specifier, but you can of course use it also there.

As egreg mentions is his comment, using >{{\raggedright}} won't work as you can see when you add more text:

\documentclass{report}
\usepackage{array}

\begin{document}

\noindent
\begin{tabular}
  {>{\raggedleft\arraybackslash}p{\dimexpr.5\linewidth-2\tabcolsep-.5\arrayrulewidth}|
   >{{\raggedright}}p{\dimexpr.5\linewidth-2\tabcolsep-.5\arrayrulewidth}}
    Kindle Edition Available & k \\
    PC/Mac Edition Available & p text some text to test text some text to test text some text to test text some text to test text some text to test
\end{tabular}

\end{document}

Using simply >{\raggedright} for the last column and \\ to change lines will produce an error since \centering, \raggedright, \raggedleft redefine \\; the array package provides \arraybackslash to restore the meaning, so the following works:

\documentclass{report}
\usepackage{array}

\begin{document}

\noindent
\begin{tabular}
  {>{\raggedleft\arraybackslash}p{\dimexpr.5\linewidth-2\tabcolsep-.5\arrayrulewidth}|
   >{\raggedright\arraybackslash}p{\dimexpr.5\linewidth-2\tabcolsep-.5\arrayrulewidth}}
    Kindle Edition Available & k \\
    PC/Mac Edition Available & p text some text to test text some text to test text some text to test text some text to test text some text to test
\end{tabular}

\end{document}