preceding it with a backslash makes it a reference to the number, which in this case has the effect of setting the max record length, this is for filesystems with record based files rather than line based files.
Setting $/ to a reference to an integer, scalar containing an
integer, or scalar that's convertible to an integer will
attempt to read records instead of lines, with the maximum
record size being the referenced integer. So this:
local $/ = \32768; # or \"32768", or \$var_containing_32768
open my $fh, "<", $myfile or die $!;
local $_ = <$fh>;
will read a record of no more than 32768 bytes from FILE. If
you're not reading from a record-oriented file (or your OS
doesn't have record-oriented files), then you'll likely get a
full chunk of data with every read. If a record is larger than
the record size you've set, you'll get the record back in
pieces. Trying to set the record size to zero or less will
cause reading in the (rest of the) whole file.