What are OVAs and how are they different from Specials?

OVA is a fickle idea, and changes it purpose from title to title. The one thing that seems to hold in most all of them is that OVA is much closer to what the original writer invisioned. Some series originally release with OVA because the writer can produce a quality high enough for public release. Others release OVA afterwards, when the project gets more funding, so it can be completed as they wanted to originally, but couldn't afford. Take it as you will.

OVAs are not special episodes, as its own name states: Original Video Animation (OVA) they were made for video consumption and had no limitations (censorship) with the intention to expand the market to a more mature audience. There's also ONA (Original Net Animation) which has been conceived to premiere in the Internet.

To describe "Special" and OVA, we need to describe what's "normal" anime.
Usually anime (TV series anime) is broad-casted weekly. It will continue 13 or more weeks. It's usually free with Television advertisement (and has eye-catch at center of episode). TV station have their code: no pantsu scene, no violence scene. The DVD (or BD) will be release later.

Special (aka TV Special) is not weekly. Usually yearly or one shot. It's have only one episode but it's have longer length (ex 2 hours). It's still intended for broadcast. Need to meet broadcast code.

OVA is created for selling (by Video or DVD). It's intended to the small number of viewer without advertisement. It means more otaku friendly theme. No need to follow broadcast code. It's OK to have hard violence scene.

But, in recent time, some OVA was broadcasting with censorship. On the other hand, some TV series is on air with censorship, and selling DVD (or BD) without censorship version. The boundary became ambiguous.

Other category is anime movie which is intended to show in theater. Anime movie is between special and OVA.

The anime Lupin the Third has all TV series version, OVA, Anime movie and TV Special. In this case, special version is yearly release.

Broadly, the two terms could be interchanged, although there are a few points of (almost) difference:

1. OVAs are generally released for home video (be that VHS, DVD, or whatever), whereas it's possible for a Special to be released as a television broadcast that is just separate from the rest of the show.
2. OVAs are often shorter than a normal episode of the show, while Specials are often as long or longer, although this definitely doesn't always hold.
3. Some OVAs are not associated with a show, so they aren't a "special episode" of anything. For example, the series Video Girl Ai was only ever released as a 6 episode straight-to-video OVA.

OVA stands for Original Video Animation, this means these episodes are much like "Beta-tests." Or they can be anything that isn't related to the Anime itself, for example; In the Anime "Clannad" there is an OVA episode where Tomoyo /Spoilers/ and Tomoya have a romantic relationship, however in the actual series this relationship does not exist, but it does within the OVA. The OVA's are separate from the series, and are usually just a little bonus from the producers, however it should be noted that they are non-canonical and should be treated as such. I hope this can help.