There are different file formats available for images, such as gif and png. Gif files are generally lower quality and are not preferable when using for a photo as your desktop wallpaper, however they are acceptable if you intend to use a repeating background image. Higher quality image formats for wallpapers such as png will result in a larger file size, however the improvement in image quality over a jpeg is minor. That is why the most widely used format for desktop wallpapers is jpeg, as it combines small filesize with a high quality image.
Depending on your screen resolution you can download different sized pictures to use for your desktop background. You can stretch the image if it is too small and it will fill up your entire desktop. But some images with different dimensions to your screen resolution will look weird if they are stretched. The best way to make sure a wallpaper fits correctly is to download a picture with similar dimensions to your screen resolution. Websites that provide free desktop wallpapers have the usual sizes to fit most screen resolutions and even if the wallpaper is stretched to fill your background, it will still look fantastic.