Okay, the term "Seelie" comes from the Gaelic "Sidhe" which means loosely translated "Light" so the Seelie Court is the "Light Court" as opposed to the "Unseelie" or "Dark" Court.  There are also stations of Low and High court fae, the High Court fae, are similar to elves, they rule and are able to travel outside of their realm for an indeterminate length of time, they can form lasting relationships with humans, and have greater powers and magic than their Low Court cousins.  Low Court fae are beings such as house elves, brownies, pixies, sylphs, dryads, shimmerlings, they usually have specific duties they must perform, and they can serve High Court fae in a variety of ways by pledging themselves in an Oath of Allegiance--the shimmerlings are messengers, for instance.  Seelie Court fae do things with contracts, like Sarai's yearly contract as Captain of Queen Titania's bodyguards, and the contract is binding for an amount of time specified and for terms that are in it.  Unseelie fae do things with coercive spells, Binding Charms that are like the Unforgivables, and that force someone or something to serve them against their will. Unseelie High Court fae are the dark elves, similar to their Seelie cousins in looks and powers, except they're the flip side. They live to cause mayhem and destruction everywhere. Some Unseelie Low Court fae are banshees, kelpies, siryns, boggarts, night hags, darkhounds, harpies, and half-men (literally half of a man, like if you sliced a body in half). 

All of that will be explained as Harry starts to learn more about the Realm of Faerie when he returns to prince Manor the following summer and Severus really starts to teach him about his inheritance.  You just happened to have a sneak peek.