Assalamu Alaykum.

Ummi when referring to the Beloved of Allah SallAllahu ‘Alayhi Wa Sallam means the one who was not taught by any man. He SallAllahu Alayhi Wa Sallam was taught directly by Allah Almighty. 

There are few reasons why the Prophet SallAllahu Alayhi Wa Sallam was titled ‘Ummi’:

1. He SallAllahu Alayhi Wa Sallam was born in Makka which is knows as Umm al-Qura (as mentioned in Surah al-Shuraa)

2. Umm means mother. He SallAllahu Alayhi Wa Sallam is the essence of the universe. From his light the universe came into existence (as mentioned in many Ahadith)

3. Means unlettered, because he did not study under anyone. As Allah says, 

“Allah, the Most Gracious.  Has taught the Qur’an [to His beloved Prophet(Mohammed – peace and blessings be upon him)].

Has created [Prophet Mohammed (peace and blessings be upon him) as the soul of] mankind.  Has taught him the knowledge [of the past and the future].” (Kanzul Iman: Al-Rahman 52:1-5) 
Imam Nabhan in his book, Jawahir al-Bihar narrates a hadith, “Umar Bin Shabih RadiAllahu Anhu writes in his book that the Prophet SallAllahu Alayhi Wa Sallam (on the day of Hudaybiyah) wrote a letter with his own hands. He never wrote before that. This is from his miracles, that without being taught how to write, he wrote a letter. Great scholars unanimously agree that it was from his miracles, likes of Imam Dhahwari, Abu al-Fath Naisapuri, Qadi Abu Walid Makki, Qadi Abu Ja’far.”
 
The Ulama have stated the Prophet SallAllahu Alayhi Wa Sallam  wrote and read before leaving the world. (Imam ‘Abrani narrating from ‘Awn Ibn Abdullah Ibn ‘Atabah RadiAllahu Anhum).
 
One of the reason he SallAllahu Alayhi Wa Sallam did not read and write so that it would become an evidence and proof against the disbelievers that the Qur’an is a direct revelation from Allah Almighty.
 
Under the verse “Wa La Takuttuhu Bi Yaminik (Surah ‘Ankabut:48), ‘Allamah Shaykh Isma’il Haqqi Alayhi al-Rahmah writes, “The Prophet of Allah SallAllahu Alayhi Wa Sallam knew the art of writing and expressed his knowledge about it.”
 
It is in the commentary of the well-known Qasida Burdah, “Sayyiduna Amir Mu’awiyya RadiAllahu Anhu narrates a hadith in which he says, “I used to write in the presence of the Prophet SallAllahu Alayhi Wa Sallam. The Prophet of Allah SallAllahu Alayhi Wa Sallam once said, ‘Keep the inkpot like this, turn the pen and make the letter ‘Baa’ straight (Aqim). Try to differentiate (Farriq) the letter ‘Seen’ and don’t bend (Ta’awwar) the letter ‘Meem’.’ He SallAllahu Alayhi Wa Sallam said this though (apparently) he did not learn writing from anyone and never read books of former people.” (Sharh Qasidah Burdah by Imam Kharputi, under the stanza, “Wa Waaqifuna Ladyhi ‘Inda Haddihimi…”) 
 
[For more detail on this topic, refer to booklet written by Shaykh al-Hadith Shaykh Muhammad Fayd Ahmad Owasi Radawi Alayhi al-Rahmah titled, “Ummi Laqab)].
 
Allah Knows Best