EIA in the horse world stands for Equine Infectious Anemia.
In the science world it stands for Enzyme-linked Immunosorbent Assay (called EIA or ELISA)
A specific type of retrovirus called a lentivirus causes the disease and there's no vaccine. Since it's so infectious, horses with it need to be destroyed in many states. Some allow the horse to be quarantined for life in an approved facility.
The test works by detecting antibodies present in your horses bloodstream to the pathogen. Coincidentally the test for EIA is performed by EIA. Kind of a strange coincidence. Confirmatory tests are done by other more sensitive methods for specific antibody detection like Agar immunodiffusion, western blot and more.
Add--http://asci.uvm.edu/equine/law/horselaw/eia.htm
Here's a good description especially of the law and requirements to do testing. The requirement to euthanize or quarantine is also discussed.
A second addition--the DonBlazer link you have above does contain some misinformation about how infectious this is horse to horse. DonBlazer seems to think that once the acute phase of the infection is over and the infected horse recovers that he cannot infect other horses. That is wrong. This person is obviously not a virologist or scientist and does not understand how a retrovirus replicates and remains in the bloodstream for life in the latent stage. While the horse is not infectious from the aspect of the horse cannot directly infect another horse through normal contact, they are still infectious through direct personal body fluid to body fluid contact (blood and saliva) and via vector animals like mosquitos or bloodsucking insects.
This is why someone with HIV is infectious the rest of their life, the retrovirus remains in the latent or chronic state. HIV is unusual in just how extremely fragile it is. HIV is so fragile that it is not transmitted by bug bites. But EIA is not that fragile. EIA is transmitted by bug bites for a short time after the bug sips blood from the host so that is why horses have to be euthanized or quarantined. Or herpes virus is another example. Once you have it you have it for life and can enter infectious periods over and over again.
And, the Coggins test originally did refer to the AGID (agar gel immuno diffusion) method developed by Dr. Coggins. It wasn't until about this timeframe that lab tests were getting much better specificity. DonBlazer was probably reacting to some of the "old school" hype of horses who had false positives by ELISA and were destroyed when perhaps they didn't need to be. That is why the AGID was developed, as a better more specific test. Every assay we use has a certain false positive and false negative rate. These are called the assay specificity and sensitivity. I could go on and on but realize most people just aren't interested in all this science speak and just want a basic understanding. But not lab test is perfect and there was a period especially during outbreaks where many valuable horses were destroyed (and some not necessarily). Today many use the term Coggins to refer to any lab test for EIA. Similar to how our culture has taken the word kleenex to describe any facial tissue. If your horse tests positive for EIA immediately quarantine him and demand a retest. Ask your vet to recommend another vet known for experience with infectious diseases and then ask that specialist for the best lab to perform the retest and by what method.
Not sure if all this extra information helps or just confuses. At some point we read and say TMI --enough already !!!!