Apostiles, which I think are probably spelled Apostilles. I've seen it both ways and autocorrect on my computer doesn't like either of them. Anyhow, they are basically an international certification. You can read all about it here, but basically it's part of the Haag convention that makes legalities more fluid between involved countries when it comes to legal documents authenticity by getting a competent part from where the document originated to say, yep, this is a good doc.
If you're not aware of the process at all, here's what I learned it is. When you get your certified document in long form from vital records, say it's your Grandfather's birth certificate in Pennsylvania, you may have gotten the certificate from ordering them directly from the Pennsylvania Department of Health (sidebar: spoke to them on the phone, very friendly and helpful! Not expected from government workers, brava!) or vitalchek or however, you need to send it off to get the Apostille.
My process was to get the certified copy of the record, scan it on my flatbed scanner (don't trust the document feeder with these documents), both sides if there's writing on the other side that isn't boilerplate*. Some of my documents has the seal on the back so I was sure to scan in everything. I would send the scan off to the translator, then get the envelope, SASE and document together to send to the appropriate Secretary of State for apostille.
When the apostille comes back to you, it's usually a piece of paper with a shiny seal and some signatures stapled to your document. Do not remove the staples! The staples hold the apostille to the document and keep it nice and valid. If you separate the two, you'll have to start all over again I hear.
My file server is off right now so I'll have to attach some copies of my apostilles later. You can go watch the video of my application, they are in there!
* What I mean by boilerplate is some lightly printed text that may be warnings of photocopying, possibly warnings that the record will not be valid if torn or mutilated, maybe some legalese about how you're not allowed to use other people's documents to, oh I don't know, steal people's identities, etc.