Contains the name of the program being executed.
On some (read: not all) operating systems assigning to $0 modifies the argument area that the ps program sees. On some platforms you may have to use special ps options or a different ps to see the changes. Modifying the $0 is more useful as a way of indicating the current program state than it is for hiding the program you're running. (Mnemonic: same as sh and ksh.)
Note that there are platform specific limitations on the the maximum length of $0. In the most extreme case it may be limited to the space occupied by the original $0.
In some platforms there may be arbitrary amount of padding, for example space characters, after the modified name as shown by ps. In some platforms this padding may extend all the way to the original length of the argument area, no matter what you do (this is the case for example with Linux 2.2).
Note for BSD users: setting $0 does not completely remove "perl" from the ps(1) output. For example, setting $0 to "foobar" may result in "perl: foobar (perl)" (whether both the "perl: " prefix and the " (perl)" suffix are shown depends on your exact BSD variant and version). This is an operating system feature, Perl cannot help it.
In multithreaded scripts Perl coordinates the threads so that any thread may modify its copy of the $0 and the change becomes visible to ps(1) (assuming the operating system plays along). Note that the the view of $0 the other threads have will not change since they have their own copies of it.