in breeding terms it's generally an animal that is used to sexually excite another animal. this can be used for either heat (estrus) induction, heat detection or semen collection.

goats and sheep especially do not exhibit obvious signs of estrus on their own, and teaser rams and bucks are needed to ferret out who is ...mmmm.... hormonally receptive and who isn't. introducing a male into a female herd will also sometimes trigger the onset of estrus, which is useful if you want all your females to be bred within a short time of each other. teaser males are vasectomized because more often than not, estrus manipulation is used in conjuction with artificial insemination. this also allows any old male to be used as a teaser, without worry that his undesirable genetics will screw up the herd.

in semen collection, "sexual preparation" through teasing is supposed to double the number of sperm cells in a male's ejaculate. the male is exposed to the sight or smell of a receptive female, then trained to mount either a live or dummy mount.

the whole point of a teaser, in other words, is to stimulate an animal but ultimately deny them any real sex. hence, the name.