Actually, white balance is adjusting the camera based on the color temperature (in degrees Kelvin) of the light that is illuminating the scene being photographed. I don't remember all of the color temperatures from my film photography days, but daylight is a certain temperature. Incandescent light is a different temperature, as is florescent, halogen, etc. Films were designed for use with a particular color of light. Usually daylight. To avoid off color in the final image (without lots of color correcting in the printing process) you needed to use filtration to adjust the color of the light hitting the film. Custom white balance is creating a custom "filter" to correct the color of the image you capture based on the color of your light as it strikes something you are telling the camera is pure white. If it is not a pure white you will end up with a mess.
To easily see how adjusting your camera's white balance setting affects your photos try the following. Go outside and during the daytime (we don't want the flash going off and altering things) and take a picture with your camera on auto white balance which is where most are usually set. Then take another photo of the same scene with the camera set to "daylight." Then another with the camera set to "partly cloudy." Take one photo for each white balance setting your camera has. When you run out of white balance settings, you're done taking photos. Go back inside, and review the photos just on the LCD screen your camera is equipped with...unless you feel like viewing them on your computer. You will easily see how the different settings change the color of your photos. The auto white balance setting will often even give you different colors from one shot to the next because it reads the scene each time you take a photo and often "sees" it differently each time, even if only slightly. You can try this test too using the above method and taking multiple photos of the same scene using auto white balance. The differences won't be as drastic, but they will be there.
The 18% grey is another matter entirely, and actually goes back to early days of photography and calibrating light meters. Most light meters average a scene to determine the exposure that will be used to get a "good" photo. Since the vast majority of photos that were taken "back in the day" were portraits, light meters were calibrated to try to get good exposures of people. In a properly exposed black and white negative, Caucasian skin is very close to 18% grey. So is nice green grass or foliage interestingly enough. This is the "norm" that light meters strive for. For years, a trick photographers used to quickly get a correct exposure for a given scene was to meter off of their hand, or meter the lawn next to their subject. I did this literally thousands of times to get the correct exposure. If a scene has too much light or dark by comparison, then your photo ends up over or under exposed because the light meter is averaging the scene. Now, in the new digital cameras, the algorithms they have used within the computer controlled light meters (many with face recognition now) are so sophisticated that they have largely eliminated this problem. Usually a small adjustment with your camera's exposure compensation setting will have you dialed in to the correct exposure if any adjustment is needed at all.
Sorry to be long winded. In a nutshell, white balance is adjusting perceived color temperature (correcting color), and a grey card is used to get a correct exposure (largely unnecessary with modern digital cameras).
