shorten < and
shorten > are not directly described in the manual as far as I can see, but it looks like they are interfaces to
\pgfsetshortenend respectively, which are documented in the end of section 99.3 Arrow Tips on a Path (manual for version 3.0.1a, dated 29 August 2015).
shorten <= <length> reduces the length of the path by
<length>, by moving the start point. For example
shorten <=1cm will set the start of the drawn line to 1cm from the specified coordinate.
shorten > is the same, for the end point.
- Using negative values will lengthen the line.
Note however that this only applies to straight lines. When the lines are not straight, the new endpoint is found on the tangential line, not along the actual path, as Qrrbrbirlbel says in a comment.
\draw[help lines] (0,0) grid (4,3);
\draw [blue,shorten <=0.5cm] (1,2.7) -- (3,2.7);
\draw [red,shorten >=0.5cm] (1,2.2) -- (3,2.2);
\draw [cyan,shorten <=-0.5cm] (1,1.7) -- (3,1.7);
\draw [shorten >=-0.5cm] (1,1.2) -- (3,1.2);
\draw [shorten >=0.5cm] (1,0) to[out=90,in=90] (3,0);
\draw [dotted] (1,0) to[out=90,in=90] (3,0);