Whether it's Pilates or Yoga, I really love teaching classes where the students have their eyes closed for the entirety of the class. This can be a little daunting for some, but there is a method to the apparent madness I assure you, and by the end of the class most students feel the benefits.
Taking it back to 400 C.E. in the Yoga Sutras of Patanjali, Yoga is said to have '8 Limbs'. These are the path to the final 8th Limb of Samadhi, or 'enlightenment'. What we practice on the mat is just one limb, the 3rd limb of Asana. The 5th limb is called Pratyahara, or sense withdrawal. Before you think that I get students to close their eyes in order to 'withdraw a sense' to get this sense withdrawal, let me explain what is meant by this. It is a sense withdrawal from focus. You've probably experienced it yourself, when you're so lost in something and someone calls your name but you've not even noticed. In contemporary times, Mihaly Csikszentmihalyi called this the state of Flow. It amounts to the same thing.
It has been said that around 50% of our brain usage goes on sight. If we take this away we're able to more clearly sense everything else around us, and more crucially in classes, in us. Close your eyes and you get a far greater sense of what is going on in your body, which in turn brings a far more concentrated focus on what you are doing. This is the 6th Limb of Yoga- Dharana, or focused concentration. This has the benefit of making your movements more mindful, but can also bring us closer to this state of Flow, or Pratyahara. This is when movement can become a meditation, which is the 7th Limb of Dhyana- meditative absorption. One class and you've nearly reached enlightenment ;) (disclaimer: If one class takes you to enlightenment you've been secretly doing all the work before class!)
I think it's also so beneficial to practice with your eyes closed because you forget about all others around you. You are in your own world so any idea of comparison disappears. You have nobody to unwittingly compare yourself to so the temptation for that goes, and over time so does the idea of 'am I doing it right?' This is such a common thought in class, and totally natural, especially when learning something new. The problem lies in that this thinking takes us away from our body's intelligence. We are in the thinking mind and removed from the feeling side of our brains. When we are absorbed in the feeling we intuitively know what is 'right' or 'wrong'. It's as simple as it feeling 'good' or 'bad'. Now when I say bad I don't mean the pain of underused muscles working- I'm looking at you, Pilates side lying series!- but bad as in something not feeling beneficial for the body.
So in class, where you can, try and close the eyes to really feel what is going on. That's where you can really tap into your body's intelligence. Enlightenment's just a little side bonus if it happens!