Expression is essential to dance. Without it, dance is boring. It becomes the equivalent of people doing "step tap" repeatedly at a school dance. It looks mechanical and lifeless. Part of learning to dance is also learning self-expression.
Not everybody knows how to appropriately express themselves, whether through words or physical means. Society has taught us to bottle up our emotions and they tend to explode out rather than coming out in a healthy slow release. This is why arts programs are important. Teaching kids how to express their emotions through art is far more effective than making them "suck it up".
As adults, the damage is quite thickly set in our personalities. Asking a new dancer to express themselves through dancing can be overwhelming and intimidating. People get scared when asked to connect with their emotions, but you don't have to go straight to the core. You can slowly peel away until you are comfortable enough to reach deeper.
Let's start at the beginning...
To help with expression in dance you must first connect with the music. Listen to lots of music and try feel with the music. I find that a good place to start is with a song that has lyrics, and then slowly move to other pieces as you begin to understand oriental music and it's various genres better. If there are lyrics, get them translated and read through it with the music. This way you can get to know the feel and tone of the music more intimately. You want to start to feel the music in your soul, to have your emotions moved as the music moves.
Close your eyes and see what images and thoughts come up as you listen to the music. Are they serene? Happy? Sad? Dark? Playful?
Imagine a dancer moving to the music. What is s/he doing? My parents took me to many classical music concerts when I was a kid. I used to imagine a ballet dancer dancing to the music so that I didn't get bored. I didn't realise it at the time, but this really helped me with connecting with and enjoying music more.
Try moving with the music like your imaginary dancer did. Try mimic or physically represent the imagery you saw when you closed your eyes. Act out what you are feeling when you hear the music. Use your whole body, even your breath. There is no right or wrong answer here, only what you feel.
Now, when you dance to the music (whether it's your own choreography or someone else), try to capture that feeling you had when you closed your eyes and imagined the music. That feeling you had when you were moved by the music.
I do recommend that if you are doing your own choreography, that you do this before you choreograph. This way the choreography lends itself to your emotions and not you placing your feelings on top of something that was created independent of expression. If you are dancing someone else's choreography, you need to find out what is their feeling for the music and try to invoke that emotion.
Even though I find it easy to connect with music, I still go through this process to ensure that the expression I give is genuine. To really sell your dance you have to be genuine. This isn't always easy, even for the most experience of dancers. You have to act the part, without it seeming acted. This is where feeling the music in the core of your being becomes so important. If you are trying to act without every part of your body and soul being committed to the role, you will not succeed.
There's even more to it than just the performance element. Dance is a healing tool. By connecting and expressing you are actually releasing emotional tension and getting in touch with your inner being. Suddenly dance is not just about getting exercise or entertaining, but it's for you and your psychological health.
As with everything in life, practice makes you better, and practicing feeling different kinds of music and expressing those feelings is important. It should be part of your dance training. It should be taught and talked about with every choreography you learn or create. Whether it's a soul shaking taqsim or a cheeky, happy shaabi, your connection and expression will make all the difference.