a.k.a. zombie box. A computer under the control of a rogue program or some type of Trojan Horse program. Zombie machines are typically used by spammers to relay spam and can be used for more nefarious purposes such as distributed denial of services attack to perpetuate online fraud or even manipulate an online poll.
Typically zombies are created by users who have accidentally run a trojan horse, or who have improper security configurations. Thus the nice grandma next door's computer becomes an outlet for potential criminal activity without her knowledge.