Backup usually means to make copies of all your files. Like your photos, mp3s and documents.
Image means a program will take an exact image (think picture) of your hard disk, this can be stored on cds, dvds or somewhere else as a big file. Then the program can take this picture of your hard disk and put your hdd back to how it was when the image was taken.
Clone, means you take another hard disk and copy it exactly to another hard disk kept as spare. So in reality you can just swap the hard disk when the other one fails.
When cloning the hard disks physically don't have to be the same size, it can be equal or bigger in storage capacity.