The $$ is a prototype; it specifies that the function WriteLog takes two scalars as arguments (see prototypes in perlsub).

In the expression @$logtext, $logtext is actually a reference to an array, and @$logtext dereferences this reference to access this array. ref is an operator that, when given a reference as argument, returns the type of reference it is (ref). To better understand ref and @$logtext see perlreftut.