As a photographer, you'll know that not all light is the same color. Well, technically, it's not a color--it's a temperature. That's one of the reasons that photos taken during golden hour look so much better than one taken from exactly the same spot at other times of the day.
For a simple way to visualize it, imagine the warm, inviting yellow and orange glow of a fireplace or golden sunset compared to, say, bright sunshine or the bluish tinge of a cold, overcast day. Our brains do a pretty good job of automatically compensating for these changes in such a way that we don't notice.
White balance is the term used for adjusting for this in digital imaging. It's derived from the idea that white provides a good reference point--what's white in the light of a golden sunset should also look white on a cold, overcast day despite the different lighting conditions.
Modern cameras do a pretty good job of detecting and choosing a white balance in their auto white balance modes. But they don't always get it right. And even what might be considered the "right" white balance might not be what you're after--it is, after all, an entirely subjective thing.
There are many times you might want to override the automatic white balance in Lightroom to tweak the look. You might want to make a portrait a little more flattering by warming it up (tilting towards the yellow and orange end of the spectrum) or make a landscape starker by cooling it down (tilting towards the blue end of the spectrum). Or you might just want to dispense with reality and create an entirely new look for the scene.
The white balance sliders in Lightroom are one of the first things you should be working with when you go to develop and image. (Lightroom's develop panels are designed to suggest you start at the top and work your way down.)
Using Lightroom's White Balance Tools
As a baseline reference, here's the starting image with the white balance settings that the camera has automatically calculated. As you can see, it's done a pretty good job. There's no obvious color cast in this case even on a heavily overcast day with a number of different tones in the scene.
But if we want to tweak the white balance, there are two parts to it.
The top slider relates to the temperature. Slide it left, towards the blue end, and you'll be making the image cooler. Go too far and you'll end up with a blue color cast.
Slide it right, towards the yellow, and you'll be making the image warmer.
The second slider relates to tint. At left is Cyan.
At right is magenta.
Using the Eye Dropper
Manually sliding the sliders is all well and good, but there's another powerful tool in the white balance kit. That's the eye dropper.
The idea behind this is that you use it a special cursor to select a part of the image that you thing should be neutral white, gray, or black. Lightroom will then use that as the reference point to calculate the shift for the rest of the image to match it.
To use it, click once on the eyedropper icon to pick it up (the cursor will change to it).
Choose a neutral gray, white, or black area that shouldn't have any color cast. Grays work best. If you choose an area that's too white or too black, you might get a warning telling you to choose another spot for better results.
The magnifying loupe view you get is helpful for seeing it on a pixel-by-pixel view.
Once you click on the spot, the temperature and tint sliders will automatically adjust to whatever settings are needed to neutralize the cast for the spot you've chose.
Sometimes the first result isn't what you want. If so, try again with a different spot.
Reseting the Sliders
If you decide you want to go back to the original settings, there's a quick shortcut. Just double-click on the "Temp" or "Tint" labels. They'll instantly revert the corresponding slider back to the original setting.
Breaking the Rules
The underlying idea of the white balance controls is to neutralize color casts. But you might not always want neutral. Maybe you want to take it in a different direction. So, by all means, break the rules to achieve whatever look you're going for.
The ability to tweak the white balance settings is most valuable and effective when working with RAW files, but the same tools remain available if you're working on JPG or TIFF files.