Classes

They are basically identifiers to select and style sections of content or particular elements. Understanding The Difference Between ID and Class might help you along. I'd also recommend keeping a good book like CSS3: The Missing Manual around for reference.

Oh, I'm referring to the iOS course. http://teamtreehouse.com/library/objectivec-basics/introduction-to-objectivec/from-structs-to-objects

He starts the project by creating a folder named "sphere_class", loads up the Xcode template, then says "let's go ahead and create our sphere class" @2:11 of the video. He doesn't explicitly give a definition of "class" and then goes on and talks about how it's separated into two files, something about the rest of the program interacting with the "Sphere class" and a separate implementation, yadi yada.

So what is it some kind of function or struct?

His heavy use of jargon is killing me!

You might check out The Beginner’s Guide to Objective-C: Classes and Objects or even some official documentation.

Also it may help to keep in mind that Apple has recently implemented The Swift Programming Language.