Current Perl documentation can be found at perldoc.perl.org.

Here is our local, out-dated (pre-5.6) version:

Hashes are pairs of scalars: the first is the key, the second is the value. The key will be coerced to a string, although the value can be any kind of scalar: string, number, or reference. If a key $key is present in the array, exists($key) will return true. The value for a given key can be undef, in which case $array{$key} will be undef while $exists{$key} will return true. This corresponds to ($key, undef) being in the hash.

Pictures help... here's the %ary table:

          keys  values
        +------+------+
        |  a   |  3   |
        |  x   |  7   |
        |  d   |  0   |
        |  e   |  2   |
        +------+------+

And these conditions hold

        $ary{'a'}                       is true
        $ary{'d'}                       is false
        defined $ary{'d'}               is true
        defined $ary{'a'}               is true
        exists $ary{'a'}                is true (perl5 only)
        grep ($_ eq 'a', keys %ary)     is true

If you now say

        undef $ary{'a'}

your table now reads:

          keys  values
        +------+------+
        |  a   | undef|
        |  x   |  7   |
        |  d   |  0   |
        |  e   |  2   |
        +------+------+

and these conditions now hold; changes in caps:

        $ary{'a'}                       is FALSE
        $ary{'d'}                       is false
        defined $ary{'d'}               is true
        defined $ary{'a'}               is FALSE
        exists $ary{'a'}                is true (perl5 only)
        grep ($_ eq 'a', keys %ary)     is true

Notice the last two: you have an undef value, but a defined key!

Now, consider this:

        delete $ary{'a'}

your table now reads:

          keys  values
        +------+------+
        |  x   |  7   |
        |  d   |  0   |
        |  e   |  2   |
        +------+------+

and these conditions now hold; changes in caps:

        $ary{'a'}                       is false
        $ary{'d'}                       is false
        defined $ary{'d'}               is true
        defined $ary{'a'}               is false
        exists $ary{'a'}                is FALSE (perl5 only)
        grep ($_ eq 'a', keys %ary)     is FALSE

See, the whole entry is gone!