The command \showthe works exactly like \the (see The \the command), with the difference that TeX stops compilation for showing the resulting token list, instead of delivering it to the input stream. So
\showthe\abovedisplayskip
would interrupt the TeX run (if found in an interactive session) printing
> 12.0pt plus 3.0pt minus 9.0pt.
l.10 \showthe\abovedisplayskip
(where 10 is a fictitious line number). In case the session is not interactive, you'll find the same information in the log file. Note that most TeX front-ends use noninteractive mode, when launching TeX.
You can see the value without stopping an interactive session or looking for it in the log file by using \the:
\texttt{\the\abovedisplayskip}
(LaTeX) or
{\tt\the\abovedisplayskip}
(plain TeX) will show the tokens delivered by \the in the PDF file.
\texttt{\the\abovedisplayskip}(LaTeX) or{\tt\the\abovedisplayskip}(plain TeX). – egreg Nov 26 '15 at 16:19