grep has no relevance here.

$|-- and --$| toggle the current value.
$|++ and ++$| set the value to 1.
$|-- and $|++ return the old value.
--$| and ++$| return the new value.

Normally, $| is set to 0.

For example,

print('$|--: '); $|=0; for (1..10) { print($|--, ' '); } print("\n");
print('--$|: '); $|=0; for (1..10) { print(--$|, ' '); } print("\n");
print('$|++: '); $|=0; for (1..10) { print($|++, ' '); } print("\n");
print('++$|: '); $|=0; for (1..10) { print(++$|, ' '); } print("\n");
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outputs

$|--: 0 1 0 1 0 1 0 1 0 1
--$|: 1 0 1 0 1 0 1 0 1 0
$|++: 0 1 1 1 1 1 1 1 1 1
++$|: 1 1 1 1 1 1 1 1 1 1
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Update: $toggle^=1 works just as well as --$|, but it's less obfuscated and has no side-effects:

$,=", ";
$\="\n";
@list = qw( a b c d );

$| = 0;
print grep --$|,  @list;  # a, c

$t = 0;
print grep $t^=1, @list;  # a, c
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Update: If you need every Nth term, try the following:

$,=", ";
$\="\n";
@list = qw( a b c d e f );

$n = 3;
$t = $n-1;
print grep !($t=($t+1)%$n), @list;  # a, d
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