Appearance and comfort
You want your headphones to not only sound good, but also look good and feel good on you. The latter is particularly important if you're going to listen to music for many hours every day. If you're working out, you'll want your headphones to sit firmly in your ears without worry of them falling out while you are moving.
There are three forms of headphones available: in-ear, on-ear, over-ear. In-ear headphones are fairly self-explanatory; the ear buds connected by a wire. They are small and go inside your ears.
On-ear headphones have a headband and cups that sit on top of your ears. Typically on-ear headphones can be more uncomfortable over very long periods of time, because they sit directly on your earlobes. However, this won't matter to you unless you tend to wear headphones for 4+ hours at a time.
Over-ear headphones are similar, but their cups are larger and sit around your ears, rather than directly on top of them. Over-ear headphones typically have more noise-cancelling properties than their on-ear or inner-ear counterparts, since they physically isolate the ear from outside sounds.
From left to right: in-ear, on-ear, and over-ear headphones.