Most digital cameras will store images as JPEGs. This file format stands for joint Photographic Experts Group, and saves image data by compressing it. The more compression (and therefore the smaller the file), the greater the loss of image quality. Users will usually be able to choose from "finer" or "normal" JPEG resolution modes on the camera, which offer more or less compression.
Some mid and higher-end models will be able to record images as other, less compressed file types, such as TIFF (Tagged Image File Format) or RAW. Because these types of files are not compressed like JPEGs, they take a lot more memory, and RAW files in particular also require post capture processing, making them a lot more work. The advantage of RAW files is that you won't lose any image data in the compression process.
Unless you're a professional photographer, this isn't really a big issue however, as the quality promised by a "finer" JPEG file should give you an excellent image quality suitable for printing your photos.