Hey felix, shooting in RAW gives you more latitude to get a usable photo. When you shoot in JPG mode, the camera takes the data off the imaging chip and processes it. It makes a number of decisions, such as how to set the exposure details (not how long the shutter was open and how big the aperture was, but what parts of the image are light and what parts are dark, i.e. brightness and contrast, and how this tone curve is set), the white balance, color saturation, and how much the image is sharpened. Then it uses lossy compression to generate the JPG file.
For most modern cameras, the JPGs out of the camera are excellent. The camera makes the best decisions for most shooters. You can set the camera on P mode and adjust the ISO to your liking and the result is great-looking photos right off the memory card. Or you can even set the camera to Auto and it will do everything. And the JPGs are relatively small files.
RAW files are much larger, because they haven't been compressed. And you have to do the extra step of using a program like Adobe Camera RAW (part of Photoshop), Adobe Lightroom, Apple Aperture, or one of the programs that come bundled or as an extra with cameras, to post-process the RAW photos into what you want. The benefit of this extra step, especially if you have a good computer and a color-calibrated monitor, is that you can make adjustments to the image that was initially recorded by the camera before any processing.
Setting the white balance is extremely easy, for example. Digital sensors can't tell what white is, so the camera has to guess, and the result is often a color cast, especially indoors or under clouds. I use a plastic gray card called a WhiBal, which costs a ridiculous 30 bucks USD delivered. Whenever I take photos, I try to take one of the WhiBal card at the same time. Then I can just click on the card in the photo with the WhiBal card and set the white balance to that photo, and the rest of the photos taken in that session can be immediately set to perfect white balance. Not a preset white balance such as Tungsten or Daylight, but the exact white balance that makes the colors correct. You can use any proper gray card for this; I like the WhiBal because it's sturdy and also has true black and white on it. Or, if you didn't take a gray card photo, you can find a neutral color in a photo and use that to get a good white balance.
You can also adjust the exposure to bring out shadow detail and blown highlights much more effectively than you can while adjusting a JPG, because all the data is still there to work with. I often reduce blown out highlights because I don't know yet how to adjust my shutter speed and aperture to stop highlights from being blown. I just shoot and deal with it later. It can't work magic, but you can usually get one stop of recovered blown-out whites or blacked-out shadows. The other things the camera does when making a JPG, color saturation, sharpening, and so forth, are also things you can set. All of this is done with the original file, which results in the best quality output, because you have access to all the data; the camera discards data it doesn't need to generate a JPG file based on its internal decisions.
All this sounds difficult, but it's actually very easy once you get used to the software. You can even make presets if you find you're using the same settings over and over for a given situation.