Tower is a bit surreal, and that appears to be the intent. You're climbing a tower, and it's not entirely clear why or how you got there. At the various levels you have to make choices that have symbolic meaning. For example, there's (Spoiler - click to show)a room full of chocolates, a watermelon and a treasure chest that fit together somehow, a suit of armor, and a room that's so bright that you can't see. I had some trouble making sense of the variety of images, though.
My original take on the game was that the PC was dead and the tower represented the PC's journey to or through an afterlife. However, the author told me that isn't quite correct. The PC is still alive. However, he had (Spoiler - click to show)once attempted suicide and is recovering. I suppose the tower can be thought of as symbolizing the PC's attempt to work through his trauma.
At the end I unlocked the code that gives you a page of text explaining what the game means, but I don't think it helped me much.
Overall, I feel like Tower is supposed to be an experience more than a story, per se. The soothing, somewhat contemplative music helps set that mood.