Do you ever get a correction from one of your instructors that you don't entirely understand? Hopefully this will help clear up any confusions!
So what does it mean when teachers say "pull up your knees!"? Well many Russian dancers use this technique of engaging the quadriceps to provide stability. By contracting your muscles, you will be able to put less weight on your knees. This is important because our knees are very fragile and prone to injury if the weight is distributed incorrectly. By "pulling up" your knees, you will be able to keep your legs straight. It also ensures that the entire range of your knees is being used and not held stiffly.
How about the correction "keep your hips straight"? If you haven't heard this one before, it can definitely be confusing. Your teachers most likely mean that you are lifting one of your hips higher than the other one. Other corrections that mean basically the same thing are "don't pop your hip" and "lift up the hip on your standing leg". The way I like to think about this one is imagine you have a ruler going across the front of your hips. This ruler should be perfectly horizontal most of the time (even when you move into passé or do an arabesque). If you can keep the ruler horizontal, then your hips will always be level.
I know one correction that I was always confused about was "lift up your arches". I wasn't sure what that meant or why we had to do it until I went and asked the teacher. When in doubt, ask the teacher at break or after class. "Lift your arches" basically means engage your feet. The teachers usually mean that your feet shouldn't be flat on the ground, but instead always working to keep balance. Your instructors can usually tell that your arches aren't engaged if there is no air under your feet. Your weight should be in the balls of your feet, so that you are always ready to go into the next move.
I hope this article has been helpful! Just remember: if you aren't sure what the teacher means, just ask them!