For a brief explanation of these settings, see my Exposure Basics.
Auto is perfect if you need a “grab shot”, or if you are in a situation where you don’t have time to fiddle with your camera settings. On the other hand, it not may achieve the result you are looking for.
Don’t get me wrong – there have been plenty of situations where I thought I could be smarter than the camera’s Auto settings, but was sorely disappointed at the results, especially indoor shots in low light. I have learned to take a shot in Auto first to see what the camera thinks is best, and then use that as a guide when I switch to Aperture Priority or Manual.