my $srcdir ='/var/local/some_dir';
my $mtime = 1;
my $destdir = '/backup/some_dir';

# Yours doesn't tell you which directory didn't exist...
die "$srcdir does not exist" unless -d $srcdir;
die "$destdir does not exist" unless -d $destdir;

print "Beginning backup...\n";

# Error checking on chdir is important too, the directory
# might exist, but not be readable by you
chdir $srcdir or die "Can't change to $srcdir: $!";

# Once your program gets bigger than a couple of lines,
# you really want to know which directories or files
# couldn't be opened
opendir ( INDIR, $srcdir ) or die "Can't open $srcdir: $!";

# if this is a big directory, slurping all the files into
# memory can be quite a waste of memory...
while ( my $file = readdir( INDIR ) ) {
    next if -d $file; # -d will be true for . and .. too
    if ( -M $file > $mtime ) {
        print "$file : Older than one day.\n";
        next;
    }
    # tar is for combining multiple things into one,
    # gzip is for compressing, since you are only doing
    # one file at a time, the tar is just wasted effort
    system( "gzip -c $file > $destdir/$file.gz" );
    if ( $? != 0 ) { die "Gzip failed" }
    print "$file archived in $destdir\n";
}