Stick, it's all well and good to get advice on what good carved turns should look like, but that alone is unlikely to move you on a path to improvement. For that, you need to focus on changes to some very fundamental movement patterns, practice exercises to build them, and be attentive to them in your runs until they become automatic. Best to pick just one thing to start, and "stick" with it.
Others have discussed the concept of foot tipping. This fundamental movement isn't apparent in your video. Adding effective foot tipping will have a strong tendency to eliminate faults that work against carving, including A-framing, stemming, small pivoting or skidding movements in turn initiation, skis drifting farther apart as the turn develops, leaning into the inside ski, and small braking actions that can rob you of the necessary speed. Rather than obsess over any such faults creeping into your skiing, start by building the new movement pattern at the level of the feet. Your body will start to figure out the upper body balancing movements needed to complement this--no need to think about that too much with the conscious mind, at first.
An excellent place to start:
Follow all the links from this page, and read the content on those pages. Lots of clear video, and exercises to practice that will strengthen the new movement.
It does take work. Good luck!