Both start with a full backup of everything, usually you would run this once a week, or in an enterprise environment every weekend.
Differential backups copy all the files that have changed since the last FULL backup. i.e. if you change 10 files on a Monday, 10 files get backup up that night. If you change 10 files on a Tuesday, 20 files get backed up that night. The restore all of the data you need the Full backup from the weekend, and the most recent Differential copy.
Incremental backups are very similar except they only backup the files that have changed since the last backup. So Monday nights backup copies 10 files, and the Tuesday nights backup only copies the 10 files that have changed since Monday and so on. Advantage being each daily backup is smaller, the disadvantage is to restore all the data you need the Full backup, and then Monday and Tuesday nights backup too. Its a royal pain in the ass to restore, and if one of those daily backups should fail you are pretty screwed.
In a business situation i would recommend backing up everything, every night onto a different location. i.e. Different Tape. When you get to the stage where the data size is too large to copy daily, i'm guessing your MP3 collection may be, then go for Differential rotation.
Its also advisable to use more than one medium to backup onto. Don't trust portable hard drives to work when you need them to, buy two of them and rotate between them on a weekly basis.