If you are moving from a point and shoot camera to a higher end compact camera or DSLR camera, then you should be very familiar with the "Auto" shooting mode, or the Green mode as it is called sometimes.
In the Auto mode, everything is pre-arranged by the camera, all you need to do is point the camera and press the shutter button, hence it is called point-and-shoot.
In this mode, there is minimum control and minimum fuss. You just trust the camera to do the work for you, select the right focus, exposure etc. Most of the time it will do a proper job, but on occassions it will miss the mark.
The various scene modes commonly found in P & S cameras, such as night scene, portrait, sports, landscape etc are also special Auto modes. They assume that you are going to shoot the subject indicated and the camera will arrange certain parameters suitable for those conditions.
So if you are moving up to a better camera, it will also be time to explore other features of the camera by moving away from the "Auto" mode, such as using the Program Mode. The program mode is the bridge from complete Auto to the creative, or more manual modes.
Play around with the Program Mode, and learn to shoot in this mode, until you grow out of it, then you can explore the other more "advanced" modes such as Aperture-priority, Shutter-priority and full manual.
In the Program Mode, you can explore taking photos with different exposure values, by simply turning the dial, and you will find the exposure values are equivalent for the same scene. This means the photos should come out more or less the same brightness but each time you turn the dial, a different apperture and speed combination is used.