I was wondering what Morrowind's difficulty slider actually does. Does it influence the damage done/received, and/or your succes chances with everything, or what?

As you move it to harder, it reduces the amount of damage you inflict, and increase the damage you recieve. Going easier reverses this. Other than that, not much difference in the game.

Since Morrowind is a skill use character progression, some have cranked the difficulty up to max and gone hunting Mud Crabs with a Rusty Dagger. Lots of hits, lots of skill progression. However you end up with an unbalanced character that does not play well with the rest of the game as your other skills are not up to the challenge.