Learn Spanish (Spain): Mi hermano lleva gafas.

In Spain, llevar is the most common verb used for wearing clothes, accessories, and even hairstyles. While it does mean "to carry" in other contexts, when applied to things on your body like gafas, it translates to "to wear."

Could I use the verb usar instead of lleva here?

Yes, you can use usar (to use or wear), and you will hear it often, especially in Latin America. However, in Spain, llevar is the much more natural and common choice for talking about what someone is wearing right now or usually wears.

Why doesn't the sentence say lleva unas gafas to mean "wears some glasses"?

Just like in English, you do not need an article here when talking about the general state of wearing glasses. You just say llevar gafas. You would only use unas if you were describing a specific pair, like lleva unas gafas rojas (he is wearing some red glasses).

I learned the words lentes and anteojos for glasses. Is gafas different?

They all mean the exact same thing! Gafas is the standard word used in Spain for eyeglasses. Lentes and anteojos are widely used in Latin America, but in Spain, you will almost exclusively hear gafas.