A "teaser tom" is a sterile tomcat that cat breeders rent to service their kitties so that their heats will end.
For cat breeders, letting their queens go through estrus cycles unsated is a bad idea, as it can lead to problems such as constant wailing, aggressive behavior and cystic ovarian disease (the cat can't release her eggs unless she's stimulated with something approximating the barb on a tomcat's penis). However, cats are promiscuous animals and have heats many times a year; even the busiest breeder won't want his or her cat having that many litters. Hormonal estrus suppression medications like Ovarid (megestrol acetate) cause a host of health problems like cancer and diabetes, so many breeders turn to teaser toms.
Teaser toms are selected for having the same behavioral and physical qualities of a good stud cat: he must be young, in excellent health (his vaccination record must be spotless), pretty, have plenty of stamina, and be gentle and good natured. Unlike studs, teaser toms usually have some pedigree flaw that makes them unsuitable for breeding.
Teaser toms are sterilized by veterinarians who give them a vasectomy instead of the standard neutering. Thus, the tom emerges with his testicles (and masculine instincts) intact, but without the ability to father kittens. A teaser can get right to work about six weeks after his surgery.
Teaser toms are something of a rarity, so a teaser may actually get far more clients than a top-rated stud.
If you seek the services of a teaser tom for your lovelorn kitty, be prepared to spend a pretty penny. You will also have to show proof that your cat has been properly vaccinated, dewormed, de-fleaed, and has had her claws trimmed so she won't slash the feline gigolo you've brought her.