Ibn `Abbas (May Allah be pleased with them) reported: Messenger of Allah (PBUH) said, "When one of you finishes eating, he should not wipe his fingers until he has licked them himself or has given them to someone else to lick for him."[Al-Bukhari and Muslim].
Messenger of Allah (PBUH) instructed his followers that after taking meal they should lick up their fingers before they wash or wipe them with a towel. Or they may get them licked by somebody - wife, son or disciple - provided he or she feels no aversion to doing so. Since Messenger of Allah (PBUH) approved of this act, it is commendable. As to its rationale, the subsequent Ahadith will offer exposition.