An exposure with flash is basically two exposures which you combine. One exposure is for the ambient light. One exposure is for the additional light from the flash. Once you understand that, and figure out how to control the two exposures independently, you can then balance your lighting to get (almost) whatever effect you like. The skill is in finding the right point of balance.
If you ignore flash, for a moment, and just consider regular autoexposure, you have the Exposure Compensation control, which you can twiddle to make the exposure brighter or darker. When you use flash you have an equivalent control - Flash Exposure Compensation - that allows you to brighten and dim the flash part of the exposure in the same way.
However, what you tend to find in the real world is that for party/wedding scenes especially, the reflectivity of your subjects keeps changing with each new shot and composition. This makes it a nightmare to keep tweaking EC to compensate for the changing subject/scene. By contrast, the overall ambient lighting is normally pretty even across most of the room. By using manual exposure to control the ambient light you have one element of your photography to stop fussing about. It's enough to be thinking of composition, timing, focusing and flash control from one shot to the next without also having to fiddle with your ambient exposure. So, set up a solid manual exposure for the ambient lighting and just tweak FEC to fine tune the contribution from your flash.
That's the exposure side of things dealt with. That still leaves the quality and direction of the light to consider. I won't go into detail on that but the long and the short is that....
- a small light source, like a flashgun on its own, creates very distinct shadows, with hard edges. These can look really ugly when they fall visibly onto whatever is behind your subject. By making the source of light (much) larger, the light will wrap around your subject, partially filling in the shadowy area behind your subject and making the shadow edges soft, the shadows themselves less dark, and generally looking nicer altogether. Two main ways to make the light source appear larger are to use some sort of diffuser, like a softbox or umbrella, or to bounce the light off a wall/ceiling or both. For event type photography on the move I don't think that softboxes and umbrellas are very practical, so bouncing is the technique preferred by many.
- There is also the matter of the direction of the light, and distance from camera as well. If the flash is too close to the lens you may get redeye, so firing the flash straight at your subject from the flash gun is not ideal, plus there is the matter of nasty shadows in the wrong place too, especially when you shoot in portrait orientation and the flash ends up beside the camera. Side lighting is good, to create an impression of depth, with some shadows and highlights upon the subject, but not if there are harsh shadows, and you won't get much effect with the flash only a few inches from the lens.
So, by bouncing the flash you gain the advantage of enlarging the apparent source of the light, before it strikes your subject, plus you get to fill in behind your subject so the unwanted shadows pretty much disappear. By choosing your bounce angles carefully (think of bouncing a snooker ball off a cushion) you can achieve some directionality for the light, to enhance shapes a little, without the hard contrasty light you might otherwise find.
If you want to have a play around with bouncing then have a look at this website for some ideas for constructing your own flavours of bounce card....
http://www.abetterbouncecard.com/
I'm afraid some of the videos are agonisingly drawn out, but if you can bear with them you might learn some useful stuff.
More good stuff here -
http://www.youtube.com/watch?v=Xnn5nzPvoIM.