This is answer is inspired by Philip Klöcking's comment, and part of it was originally posted here
Yes subjective experience can be described, even though the description of the experience and the experience itself are different. The difference between the subjective experience itself and it's description is illustrated by the concept of qualia.
Here's an example that demonstrates what qualia is: Imagine a dentist called Mary, who is the top dentist in her field, she has aced every dentistry topic there ever was, can cure any patient who comes to her with a dental problem no matter how bad that patient's condition, and has studied every biological, neurological and chemical aspect of what a toothache is. In short she knows everything there is to know about toothaches. However, she has been an avid tooth brusher ever since she was a kid, and she has never ever had a tooth ache in her life. A dualist will argue that because of this, she doesn't really know what a toothache is at all. She knows all there is to know about toothaches, but she doesn't know what a toothache is, having never had the feeling herself. This difference between knowing everything about something, and knowing what something is or how it feels, is what philosophers of mind call qualia. Dualists think that qualia is proof that there is a non-physical dimension to the mind, since if the mind were purely physical, there would be no difference between the "about" and the "is".
So there can be an informal or ordinary language description of pain. And there can be a more detailed and comprehensive scientific description of pain as well. Dentists and Doctors use the description of of pain to diagnose patients all the time "Can you describe your pain?" "I feel a constant throbbing in my left jaw" "Oh - I think you have cavity in your left tooth.". And yet pain remains the ultimate subjective experience.
Note that qualia are used mainly as an argument for dualism. Regardless of whether the concept does indeed prove dualism (I personally don't believe this), the explanation above does show how something can be both subjective and describable, and what the difference between the experience and the description is.