Naat Sharif is a way of praising and giving tribute to Holy Prophet (PBUH).
Every Muslim he/she must love and respect the last Messenger of Allah more than his/her Life, it is obligatory on all.
"Naat" word refers to "Poetry", it is quite popular in Asia (India, Pakistan, Afghanistan and Bangladesh) commonly in Urdu, Punjabi, Arabic, Pashto, Bengali and English language. In Arabic "Naat" is usually called Madih (praise) or nasheed (poetry). The person who recites Naats called Naat Khawan.
Hassan ibn Thabit (RA) was the first Sahaba who started writing and reciting Naat (Poetry) in honor of Prophet Muhammad (PBUH). He was also Islam's first religious poet (Naat Khawan).
I asked Abu Huraira "By Allah! Tell me the truth whether you heard the Prophet (SAW) saying, 'O Hassan! Reply on behalf of Allah's Messenger (PBUH). O Allah! Help him with the Holy Spirit." Abu Huraira said, "Yes ."
-Sahih al-Bukhari 453
Al-Bara' bin `Azib (RA) said (through another chain of sub-narrators):
"On the day of Quraiza's (siege), Allah's Messenger (PBUH) said to Hassan bin Thabit, 'Abuse them (with your poems), and Jibril is with you.'"
-Sahih al-Bukhari 4124
"Tala al Badru Alayna" a Naat (poetry) or (song) sung for the Prophet Muhammad (PBUH) during his completion of migration to Medina in 622.
Click here to see the list of Sahabas whose Naat Khawani is Recorded in Hadith.