Attahiyyaat is a very important ‘Dua’ we repeat it in our daily prayers.
When I came to know the background, it actually melted my heart. 
Attahiyat is actually a part of a conversation between Our Creator Allah SWT and our beloved Prophet Muhammad (pbuh) during his journey of Al Isra Wal Miraj.
When Prophet Muhammad (pbuh) met Allah SWT, he didn’t say ‘Assalam aleikum’.
What is someone going to say when he meets Allah SWT ?
We can’t wish HIM peace because ALL sources of peace are through HIM.
So Prophet Muhammad (pbuh) said:
“Attahiyyaatu Lillahi Was Salawatu Wattayyibatu”
(All compliments, all prayer and worship are for Allah)
Allah replied:
“Assalamu Alaika Ayyuhannabiyyu ‘Warahmatullahi Wabarka’tuhu”
(Peace be upon you, Oh Prophet and Allah’s Mercy and Blessings).
To this, Prophet Muhammad (pbuh) replied:
“Assalamu Alaina Wa’ala’Ibadillahis Saa’liheen”
(Peace be on us and on all good slaves of Allah)
