In unix based systems the items starting with a dot is hidden when listed. Note the famous website name Slashdot. I think, this is kind of an homage to or imitation of that behavior.
Usually the keys can be comprised of folder like structures, e.g., when you use \tikzset{line width=1pt} it is roughly equivalent to
\pgfkeys{/tikz/line width=1pt}
As you can see there are no dots involved. This is because line width is an exposed key of the tikz key family. However certain keys have their handlers very much like what hidden files in a folder serve. These are called handlers and start with a dot such as .style, .code, .value required and so on.
In combination, it looks like the dot belongs to the slash but it actually belongs to the handlers. Handlers are too long to be explained here but since you get the notation idea hopefully you can read about them a bit better in the manual.
For the \tikzstyle please have a look at Should \tikzset or \tikzstyle be used to define TikZ styles? and try to switch to \tikzset instead.
pgfkeys? ('Key management', page 875 in the current manual) – Joseph Wright Oct 19 '16 at 11:54