A spec script is short for a "speculative screenplay." In the television medium, this is a screenplay that is written not necessarily with the intention of being produced, but more often than not for the purpose of gauging the talent of a prospective writer. Spec scripts come in two forms--solicited and unsolicited. A solicited spec script is usually written at the request of a producer who has already had contact with the writer and who wants to see more of his work. An unsolicited screenplay is one that has been sent to a producer at the request of nobody in particular with the hopes of it being read and leading to a job.
The effects of a spec television script can be many. A well-written and positively received spec can lead to any number of positions on the staff of a television show. A writer may be selected to become a pertinent, paid part of the writing staff. She may also be asked to work freelance, polishing or writing only a few scripts over the course of a season. A good spec may not lead to a job right away, but it could cause a writer to stick in a producer's mind when the need arises for writers later on.
A poorly written spec will result in no job offer, as well as a virtual guarantee that a person will not get a writing position for that particular show for the rest of its existence.
There are many ways to help write a good spec script. For starters, do not write a spec for your own, fictional show. It is a waste of time, as it will not be read. Write a spec for an established, well-known show. Watch as many episodes of said show as possible to get a feel for the way characters talk and act, as well as the general scope of its stories. Write as standard an episode of the show as humanly possible. Do not make your episode about new characters or locations that you've created that stray from the norm, as it will not be a good example of how well you can adapt to the already established voice of a show.
One common misconception about sending out spec scripts is that you should send a spec of the show you want to write for to that show. This isn't a good idea. For starters, the creative people at the show in question are legally advised not to read any specs for their show because if your spec happens to be similar to an episode they have in production, that could open them up for a lawsuit. More important, however, is the fact that they are often much too close to their own show to be able to forgive any first-time mistakes you may make with their characters. Write a spec for a similar show that is well known that producers will probably be familiar with, and send it to the show you want to write for.
Any spec you send out should be sent with a polite and humble cover letter detailing your intentions and containing your contact information. It is very important to be polite in this letter, as it will be any producer's first impression of you as a person. Writing "your show stinks, and I know how to fix it" is an easy way to get your script thrown in the garbage. "I love your show and would be honored to be a part of your writing staff" is a much more useful approach.