Even in "manual" mode, unless you're using a dedicated light meter, your camera is offering "advice" on how to expose the shot via the information you can see through the viewfinder.
At the root of it all, the camera "meters" the shot. You can change the metering mode to tell the camera to be specific as to the metering at some point OR allow the camera to evaluate a larger area -- but in the end, the metering determines the overall exposure value that the camera wants.
If you're in auto mode, the camera is still going to use the exposure value dictated by the meter and the computer will set the shutter speed, aperture, and ISO setting.
For any given value of light, there are probably a half dozen valid combinations of the f-stop and shutter speed alone -- AND add to that that your camera has 3 or 4 different ISOs that might actually look pretty good... and a few more if you're willing to put up with a little noise in the image. In total you have dozens of ways to combine the three settings and still collect the same amount of light on the sensor.
This might lead one to wonder ... how does the camera decide what to use in full auto if there are actually dozens of valid combinations that work?
The answer is... they don't all _really_ "work". They all collect the correct amount of light... but there's a big difference between the "correct amount of light" and a "sane exposure" setting.
By this I mean that you could pick shutter speeds that are MUCH too slow for a hand-held shot, or you could pick a shutter speed that's MUCH too high and forces the camera to crank up the ISO to the point that you have excessive image noise.
This is what Keith means when he says you not only have to know how the exposure triangle works... you have to understand the "nuances". Although you can technically pick any value (the camera will let you), there are consequences which will impact the quality of the photo. Not only may the setting you dial in be detrimental, but it may also force the computer to pick a setting for one of the other parts of the exposure triangle which are detrimental as well.
When the camera gets to do everything on full auto, the computer tends to seek "happy medium" settings because they tend to be safe. But safe settings are not necessarily creative.
I don't always shoot on manual. I will WHEN the lighting is steady. Usually that means the lighting is naturally steady, or I'm controlling the lighting, or I'm directing the subject and can put them in the lighting I want.
If I can't be in control, I might go for a semi-automatic mode such as Tv or Av mode... that way I don't have to keep dialing the exposure up and down while the lighting around me changes rapidly. I use Tv mode only because I need to maintain a minimum shutter speed (usually to freeze action) OR because I want to force a slower shutter speed to guarantee that my shot will imply motion by allowing some motion blur to show up in the image (such as a "panning" shot or a "creamy" waterfall shot.) If I'm not trying to do one of those two things, I'm probably not going to use Tv mode. I'll use Av mode to force either a shallow or broad DoF. I might also use it to force the lens to a sweet spot on image quality (most lenses yield their most optimal visual acuity at about 2 stops down from whatever 'wide open' is.)
REGARDLESS... be aware of the sane limits of an exposure. Just because you CAN dial in an exposure that the meter says will create the proper exposure value for the present light doesn't mean it'll look good.