Why? As a lifelong student myself, I always like to explain why to the best of my ability.
So here it goes...
Firstly, on the grossest level, being barefoot means you can see your feet better. Having socks on, you can see the general shape of the foot, yes, and it is much more intimate than having footwear of some kind on, but you cannot actually see your foot. The feet are very important in yoga, believe it or not. This is the foundation for many of your poses. So, you want to see and feel and understand the foundation in order to build onto that foundation, just like if your were trying to construct a building. What good would it be for you to try to put walls and a roof on something when you have little knowledge of the floor of the building?
Next, on top of seeing your feet, you can feel your feet much better if you are barefoot. When your feet can make contact with the surface beneath you, it will allow you to feel more grounded. You will find, in time, that you can actually begin to connect to the different areas of your feet than you ever imagined. This is going to be tremendously beneficial for everybody, but especially for those with any sort of foot issue, such as flat feet or high arches (more on this another time).
And lastly, there are more subtle reasons why you would like to be barefoot. Allowing the flesh on the soles of your feet to make contact with the same surface you are practicing on will keep you more connected. There is an energy that flows through your feet, undoubtedly. You have so many nerve endings in the feet and the hands (which is how you can explain reflexology) and allowing those nerve endings to be stimulated by letting them touch and feel and make contact with surfaces is enormously beneficial. Being barefoot means just one less material or surface between you and the earth beneath us. And yoga is about unity; unity with body, mind, soul, spirit, and the universe.