This phrase is a reference to the memorable Sorceror's Apprentice scene from Fantasia in which Mickey Mouse, playing the eponymous hero, attempts to conjure up a broom helper, and ends up with an entire army of broom automatons.

On some e-mail systems, you can set up an automatic reply for all incoming mail (often called a "vacation message"). Before doing this, however, you need to unsubscribe from or suspend all mailing list activities. That's because, in some rare cases, the automatic reply to a list message will get sent out to the entire list membership. Since you're a member of the list, you'll get your own reply, which will generate another automatic reply to the entire list, and so on until many teeth are gnashed and much hair is pulled.