One of the things that I like about SYTYCD is that they don't spend a lot of time defining, for those in the general audience, the dance terms they use. They seem to assume that those who are really interested will ask someone who knows.
If you're serious about dancing, it's helpful to learn the language. Not just the physical language, but the terminology. What is first position, second position, fifth position? What is a jetée, a rondé, an arabesque? What's the difference between an arabesque and an attitude? What is a pirouette? What are chainé turns, pivots, swivels? What, exactly, is an extension?
These terms are used as a matter of course in ballet, jazz, and modern dance classes, but you may not hear them very much in ballroom or other partner-dancing classes. Which is kind of a shame, because most of us learn in an environment of words.
If a teacher can say "take fifth position, right foot back" that's easier than saying "place your right foot behind your left foot, right toe to left heel, both toes turned out." The dance term provides a shorthand.
I try to introduce and use dance terminology when teaching, for that reason. The same goes for figures: it's a lot quicker and easier to say "forward half of a box" than "left foot forward, right foot to the side, left foot closes to right foot."
One of the great things is that all of these bits and pieces of knowledge can be studied outside the dance class or lesson. As I've mentioned before, there are so many educational supplements available now, from printed manuals to DVDs to popular books, that a really interested student has plenty of resources.
There is no such thing as too much information. The more you learn outside the class or lesson, the less you have to think about during the class or lesson. All you have to concentrate on is what's immediately before you.
And because every teacher presents information differently, learning basic terminology on your own will give you a base upon which to build, and to which you can relate what you're getting from your teachers.
Remember, you have to have a vocabulary before you can construct a sentence. Same goes for dancing. Learn the proper vocabulary, and your constructions become simpler, more clear, more definite and more intentional.
Otherwise, you risk putting yourself in a position only because someone tells you to, which is not the way to create beautiful movement. If you know what you are doing, and can put a name to it, your movement is more intelligible. From my observations, you will also find it easier to remember sequences of movement.
Not to mention, you'll be able to point out which sensational action the latest SYTYCD contestant just pulled off. It's all part of considering yourself a dancer.