There are 3 types of headphones: Circumaural (over-ear), supra-aural (on-ear) and in-ear (IEMs/canalphones). Over-ear generally refers to the first type, and are different from IEMs.
Circumaural: Generally very large and designed to fit completely over the ear. The speakers themselves are recessed behind padded cups. These are often preferred because they offer greater isolation and tend to be more comfortable for long periods of listening. Circumaural phones tend toward the higher end of the price spectrum because they're most desirable for studio use, though there are plenty of consumer models available.
Supra-aural: These are your smaller cans and are designed to rest flat on top of the ear. These tend toward the low to midrange as they're not designed to create a seal, leak a lot of sound, and provide no isolation from outside noise. You can get noise-cancelling cans like these but I'm not a fan of ANC at the best of times and I find they are lease effective on this type of headphone. Still, you can get some pretty good supra-aural cans. I use Grado SR60s for my home listening and they're great.
In-ear monitors/canalphones: These are designed to fit inside the opening to the ear canal. They tend to be very small and fit snug inside the ear using either silicone or foam sleeves.
It might be that you've heard "over-ear" in reference to IEMs for one of two things:
1: They come with hooks that hook over the top of your ear to provide some protection against them falling out.
2: Most IEMs are inserted in the ears by wrapping the cord over the top of your ear (back to front) and inserting them from above the ear, rather than inserting them straight with the cord hanging down. This method provides strain relief for the cord and keeps them in your ears easier since the weight of the cord is pulling on the top of your ear rather than the phones, and it helps eliminate cord noise from the cord dangling around.
Hope that answers your question.
