The answer to that question can both fill volumes, and be answered in a single line: A good level is a fun level. Victor Hugo wrote "If a writer wrote merely for his time, I would have to break my pen and throw it away." That is to say, don't design just for the simple sake of designing a level. Rather, design a level to be used. Give the level purpose, motion, and character, and it will be a good level. All aspects of design will contribute to that, and must be balanced against each other. In the end, people are going to judge the level on whether or not they liked playing it.

 » Purpose
A level with purpose draws the player in. It both gives the player a goal, and creates the sense that something is being accomplished aside from and apart from what the player is doing. This can be loosely termed as realism, although that may be too broad of a word.

 » Motion
Give motion and momentum to your level in both a physical and temporal sense. I'm referring less to doors, trains and buttons, and more to the motion of consequences. By looking at a level, you should be able to know, or at least guess, what has happened before you arrived, and at least have an inkling of what will happen in the immediate future. Give the player a sense that he is running through a living area, where things happen.

 » Character
This can be used to describe the lighting, the structure, the relative ambiance of a level. The character of a level can determine, and is partly determined by, its purpose and motion.

No single piece of a level can be classified under one of the above categories, but falls into all of them at once, or rather, none of them, unless considered with each part of the level as a whole.

- (Roark) Ayn Rand, The Fountainhead.