Headphones are a studio must. I use them for all of my online lessons; it allows me to hear details of my students singing voice and, for many software applications, is necessary to prevent feedback.
I find that open back headphones are the best for online lessons and teaching. I can still hear myself, my piano and my singing naturally while also still hearing either my teacher or my students in my headphones. Expect another review of close-backed headphones- the best when you want to listen to your recordings- block out all the noise around you and hear only what your recording equipment captures.
In this review, I discuss a few top brand headphones, including ones by Audio-Technica, Philips, Sennheiser and Beyedynamic. My largest tip? Buy them used. Audiophiles know that the speakers in the headphones have about a 30 hour burn in time to sound their best, so used is actually generally a better sound and a much better price.