I'm a dancer, so I tend to view dancing a bit differently than a lot of people (I tend to be so into it that I start dancing in my seat). If you're looking for a description from a dancing perspective, the moves are far less important than how it feels and what we're trying to get across. This is true even in super structured dancing like classical ballet (my specialty, though I did take a class in belly dancing). Part of your brain is analyzing and controlling, and part is in the performance. When I write scenes about dance from the dancer, I focus on things like breathing and heartbeat, on the feel of the music and what it brings out, on the emotions that dance demands of me.
Someone watching is only a bit different. For that, I focus on the overarching parts of the dance. For something with a lot of movement and colorful costumes, maybe it's the way the silk swirls and trails behind them. For something with a lot of little control, maybe it's the way the dance draws you deeper in, drawing your attention closer until that inevitable moment when it just stops or when it gets big and explosive again. There's a style of 'belly dancing' (such a broad term) where the dancers wear large and loose costumes and then only make small, controlled movements in their torsos. At first, especially to someone unfamiliar with the style, you hardly see anything. You look closer and closer at the same time as the movements get bigger, and it creates a very mesmerizing, intimate feeling. In another style, the dancer is seated and entirely covered but for her hands, and her hands do almost the entirety of the dancing (it's one of my favorites). There's still emotion, but a different sort than the dancer experiences.
In all my years, on either side, the least important part of dancing is the moves. The emotions and story of the dance are the reason that many people dance. Write that, and the scene becomes engaging.
You could also do a hybrid approach. Start out more clinical and focused on choreography, and then move to more and more emotion and story-based as the MC gets closer to it, if they started out unfamiliar with it.