The above "old name" expression from left to right does...........
([0-9][0-9]_)
Represents 2 numerical digits on the left of the file name followed by an underscore. Because the expression is enclosed in () it can be referenced in the new name by \1. Since you did not want the numbers in the new name, \1 was not included in the new name
(.*)
Represents anything. Note that it too is enclosed in parenthesis and which means it can be referenced in the new name by \2 which Zippo does.
(-)
Represents just what it looks like, an underscore followed by a dash followed by another underscore. Again he enclosed it in parenthesis and it could have been referenced in the new name with a \3
(.*)
Represents anything. Note that it too is enclosed in parenthesis and can be referenced in the new name by \4 which Zippo does.
((.*))
Represents an underscore followed by an ( followed by anything followed by ) followed by another underscore. This match could have been represented in the new name by \5
(.mp3)
Represents the .mp3 file extension and was represented in the new name by \6