When anyone of you eats food, let him not wipe his hand until he licks it or has it licked.
Authentic hadithعَنْ ابْنِ عَبَّاسٍ رضي الله عنهما أَنَّ النَّبِيَّ صلى الله عليه وسلم قَالَ: ««إذَا أَكَلَ أَحَدُكُمْ طَعَامًا فَلا يَمْسَحْ يَدَهُ حَتَّى يَلْعَقَهَا، أَوْ يُلْعِقَهَا».
Ibn ‘Abbās (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) said: "When anyone of you eats food, let him not wipe his hand until he licks it or has it licked."
Explanation
The Prophet (may Allah's peace and blessings be upon him) ordered whoever eats not to wipe his hand or wash it until he licks it or has it licked. The reason for this, as some narrations state, is that one does not know where the blessing lies in the food. Therefore, the Prophet (may Allah's peace and blessings be upon him) ordered licking one's fingers, because the blessing may be in the traces of food on fingers.
Source · Narrated by Bukhari & Muslim
From the Hadith Encyclopedia (hadeethenc.com).