Shooting with RAW files (in stead of jpeg) means that the photos are not processed by the camera, and contain a lot more information compared to a jpeg. Working with RAW, gives a lot more flexibility in processing your pictures. Mistakes made (although they should be avoided, if possible) while taking your pictures, are often easily corrected in Lightroom or Photoshop when shooting in RAW. RAW also gives a lot more leeway in your creativity, giving you the opportunity to go crazy with colors with (sometimes) incredible results. See for example the following pictures:
A disadvantage is that you have to proces each photo individually. This takes a lot more time, but the results are worth it, is far as I'm concerned. I only shoot in RAW, because editing the photo is just as imported (and fun!) for me as shooting is.
For some tips and tricks I can recommend the youtube videos of Serge Ramelli: