When you see people doing amazing moves, it's the flow and grace that captures your attention. When your moves become easy to do then you feel like you are flowing in your dancing. When you first start dancing, or doing a type of dance that you are unfamiliar with, your body isn't used to doing those types of movements. Your muscles aren't used to working in those ways so it will feel awkward at first.
Think of moves you do all the time. Walking, smiling, brushing your teeth or doing your hair. Any move that you do all the time will feel easy to you because you are familiar with it. And that's how you find flow and grace in your dancing, by becoming familiar with the patterns for making certain moves. This comes with repetition and practice – of course. But I also think just as important as repetition is the chance for your body to integrate what it has learned.
Repeating moves to the point of fatigue takes your awareness away from how you are moving because the end goal is to 'do the move' rather than understanding how your body is moving. Rather than this, I find a great way to practice is by doing moves slowly and with awareness at first, which gives your body a chance to understand new patterns. However, once it has felt the motion of a new pattern, taking a break will allow all those new ways of moving to be integrated by your body. When you come back to it the next day, you will find that you really do remember how to do the moves you were working on earlier and you can build on that.