@$r is the same as @{ $r } .
$r is an array-reference ... adding the @{ } around it converts that into an array that can be iterated.

'map' will "transform" each element of the array, returning a modified array.

The "transformation" is in the form of a regular-expression - in this case, it extracts "word" type characters (\w), decimals (.) and so on. See perlre.

The result of this map is stored in the array @cols, which is later printed.

Hope this helps. If still unclear .. experiment, and come back with more specific questions.