Sending the result of an opertation to $null simply causes it to be discarded.
All of these are functionally the same:
$null = remove-item "$destzip\*" -recurse -force
remove-item "$destzip\*" -recurse -force > $null
remove-item "$destzip\*" -recurse -force | out-null
You use this when an expression will produce output to the Output stream that you don't want, to keep if from polluting the pipeline. I'm not sure why it's being used in your example, since Remove-Item doesn't produce any output.