Hadith: The Messenger's right hand was for his purification and eating, and his left hand was for cleansing after relieving himself and (handling) repulsive things.

عن عائشة رضي الله عنها قالت: "كَانَت يَدُ رسُولِ الله -صلَّى الله عليه وسلَّم- اليُمنَى لِطُهُورِهِ وطَعَامِهِ، وكَانَت اليُسْرَى لِخَلاَئِهِ، ومَا كَانَ مِنْ أَذَى". عن حفصة رضي الله عنها "أَنَّ رَسُولَ الله -صلَّى الله عليه وسلَّم- كَانَ يَجْعَلُ يَمِينَهُ لِطَعَامِهِ وَشَرَابِهِ وَثِيَابِهِ، وَيَجْعَلُ يَسَارَهُ لِمَا سِوَى ذَلِك".
[الحديثان صحيحان] - [الحديث الأول: رواه أبو داود وأحمد. الحديث الثاني: رواه أبو داود وأحمد]

‘Ā'ishah (may Allah be pleased with her) reported: The Messenger's right hand was for his purification and eating, and his left hand was for cleansing after relieving himself and (handling) repulsive things. Hafsah (may Allah be pleased with her) reported that the Messenger of Allah (may Allah’s peace and blessings be upon him) used his right hand for eating, drinking, and getting dressed and used his left hand for things otherwise.
Sahih/Authentic. - [Abu Dawood]

Explanation

‘Ā’ishah (may Allah be pleased with her) tells us what the Prophet (may Allah’s peace and blessings be upon him) used his right hand for and what he used his left hand for. She says that he used his left hand for handling repulsive things, such as cleansing his private parts after defecation or urination, whether with water or with a solid substance, sniffing water into the nose, blowing it out, and the like. For everything else, he used his right hand in order to honor it, since the right side is preferred to the left side. This Hadīth is among the proofs of preferring the use of the right hand in doing honorable things. ‘Ā’ishah (may Allah be pleased with her) said that he used his right hand for purification, meaning that he would start with the right side in ablution or bathing by washing the right hand before the left and the right foot before the left. As to the ears, they are considered one organ included in the head, so they were wiped at the same time (the right ear with the right hand and the left ear with the left hand). If someone can only use one hand, then he starts with wiping the right ear. The Prophet (may Allah's peace and blessings be upon him) also used his right hand to eat and drink. He used his left hand to cleanse himself after answering the call of nature and handling other filth such as spittle, nasal mucus, and lice. The Hadīth reported by Hafsah confirms the Hadīth of ‘Ā’ishah in recommending the use of the right hand in doing what is honored and the left hand in handling what is considered filthy and repulsive, such as performing Istinjā’ (cleaning with water) and Istijmār (cleaning with a solid substance),and the like.