Over ear surround the ear and are larger. They usually block sound a little better. On ear sit "on the ear" and tend to be smaller, with less sound isolation. I have glasses and I find on ear to be a little less comfortable than over ear
I believe on ear headphones are smaller. Around ear completely covers your ears and hugs the sides of your face. On ear usually doesn't completely eat your ears up. Around ear would probably seal better for most people but tends to get hot more quickly than with on ear. Frankly I can't tell any difference in audio quality between good on ear and around ear headphones, as long as it fits correctly. I think it just comes down to fit and comfort, personal preferences.
With over ear your headphones actually fit over your ears so the padding touches the area on your head around your ears. With on ear headphones the padding just rests on your ear without touching the side of your head.
Over the ear sit on the area around the ear, on the skull, whereas on the ear headphones rest on the ear's cartilage. I find over the ear headphones to be much more comfortable for long durations since there is a lot less pressure going against the ear.
Sometimes headphones are called "cans". Now, imagine you are putting an open can on you ear so your ear goes inside the can (don't forget to wash the can or your ear will smell fishy and all the cats in the neighborhood will hunt you :). This is "over ear". If, however, the can is not opened, your ear contacts with the flat surface of the closed can - that's "on ear"
Over ear or full sized headphones have a cup that goes over your ear.... And while bigger typically have better base..... I also find over ear to be more immersive blocking out more off the noise in the room