There is a desired luminance level for white, at a given colour temperature. There's also a desired luminance level for black (It's, well, black...) however with some crapper TFT monitors, due to the way they work, sometimes if you boost your white output the black creeps up as light bleeds though the polarising mask. That's why Kev can't get this black AND white point into spec, because as he pushes the white point up, more and more light leaks through the blacks.
Ambient light, some calibrators will tell you to adjust your environment, others will attempt to sample ambient light and adjust on the fly. Because I do all my editing after dark in my office, the lighting is constant. It's important to fit 6500K bulbs in your editing space, not dingy "warm" ones. It won't alter the calibrator's performance, but it will throw your own eyes out as you adjust for your warmer surroundings.
Once your monitor is profiled, it means that ICC profiles like sRGB now have a standard, known place to move from. The same is true of soft-proof profiles for paper too, allowing you to at least to some degree get a clue of what will or won't reproduce. It's all very approximate when it comes to paper simulation though, as obviously paper is reflective, not emissive, etc etc.
Whatever you spend on a calibrator, it won't help you much if your monitor is garbage. Even if you have a great monitor that you believe to be calibrated, learning to use the Info palette to check your image numbers is good practice anyway and helps avoid disappointment further down the line when you get your prints back.