Shama-il Tirmidhi Chapter 023, Hadith Number 002 (131).

Anas Radiyallahu 'Anhu says: "Rasulullah Sallallahu 'Alayhi Wasallam used to lick his three fingers after having eaten".

Commentary.
It was the noble habit of Sayydina Rasulullah Sallallahu 'Alayhi Wasallam to eat with three fingers only. Although we find in a few narrations that he used five fingers also. In most narrations the three fingers; thumb, and middle fingers are mentioned. The benefit of eating with three fingers is that the amount taken (morsel) will be less, and one will not eat more. Imaam Nawawi says: 'We gather from these ahaadith that it is mustahab to eat with three fingers'. For this reason the fourth and fifth fingers should not be used unnecessarily. But if such food is eaten, where it is difficult to use only the three fingers, then there is no harm in using more. Mulla 'Ali Qaari has written that to eat with five fingers is a sign of greediness. Many a time due to the morsel being big, it results in the stomach being unnecessarily strained, it is also the reason for food getting stuck in the throat.