When we talk about "cameras," it's important to remember that we're actually talking about two different things: the camera and the lens.
As a general rule, the more you spend on your camera, the more control you have over your images. A cheap point-and-shoot camera may take better pictures than an expensive DSLR if it has an excellent lens and image sensor, but the point-and-shoot won't let you control aperture or shutter speed.
Camera manufacturers typically break up their cameras into categories based on price and capabilities:
Compacts: These are small, inexpensive cameras designed for casual use. They are sometimes called "point-and-shoots" because they do not allow you to control aperture or shutter speed, but instead attempt to automatically select settings that will produce a good picture. While this can be effective in many situations, there are times when having direct control is beneficial or even necessary.
Micro Four Thirds: These cameras have removable lenses but have a smaller sensor than APS-C sized sensors (more on this later). They tend to be lighter and smaller than other interchangeable lens cameras and therefore easier to take with you.