So, I have been wondering this sense the first time I rolled a mage in a TES game. What does magic feel like? Does casting a powerful alteration spell cause great strain on your physical being? Does a destruction spell shock, chill, or heat the caster? Must one focus intensely on his target when casting an illusion spell?

In short, I was wondering if there are any in game descriptions of these things, all input is appreciated.

There are many descriptions, mostly in books and things like that.

http://www.uesp.net/wiki/Morrowind:Breathing_Water comes to mind for the school of Alteration. I'm sure others can offer other examples for the various schools of magicka.

From what I've gathered, it's almost entirely a mental thing. Casting a fireball won't burn your hand, but you can feel the warmth coming off of it. It takes concentration.