A digital camera takes pictures with a lens and shutter, just as a traditional camera does. However, instead of capturing the image on film, the light let in by the shutter strikes an array of image sensors (photosensitive cells). These devices (there are different types, but they end up at the same place) convert light to an electrical charge that is eventually stored as a pixels, a small picture element.
Digital cameras are differentiated by how many pixels the sensor contains. The more pixels, the more detailed the image will be. The more detail you have, the more options for image use and size that you have.
Since there is no film, the images are stored on reusable memory cards (or flash memory cards), which are generally removable. Additional memory can be purchased to store pictures until you download them to a PC, at which time the memory can be filled with new images.