Abu Talib was the uncle of the Holy Prophet(ﷺ) and father of Ali who became the son-in-law of the Holy Prophet(ﷺ). After the death of Abdul Muttalib, Abu Talib was given the charge of Rifadah, or collection of an annual poor tax from the Quraish in order to entertain the poor pilgrims. He was a highly respected noble of the Quraish.
On the death of Abdul Muttalib, the Holy Prophet(ﷺ) came under the care of his loving uncle Abu Talib at about the age of 8 years. He loved him both as a father and mother. Abu Talib gave precedence to Muhammad(ﷺ) his own sons. This care and protection have been mentioned in the Quran. He accompanied Abu Talib on trade visits to Syria and other places. Abu Talib played an important role in Muhammad's marriage with Khadija.
When Khadija proposed to the Holy Prophet(ﷺ), he referred the matter to Abu Talib who made all the arrangements. After the Holy Prophet's marriage, he took Ali bin Abu Talib under his care. When the Holy Prophet started preaching the new faith of Islam, the Makkans turned against him and it was Abu Talib who proved to be a strong support for the Holy Prophet(ﷺ). Though he himself did not embrace Islam. He always protected and supported the Holy Prophet(ﷺ) against the harsh Makkans.
So much so that when the Makkans imposed a social boycott on the Banu Hashim it was Abu Talib who took the whole clan (Believers as well as non-believers) to his gorge outside Makkah. This was known as the Shi'b-i-Abu Talib and the Banu Hashim stayed there for about 3 years. All sorts of relations were cut off with the family who lived a very hard life in the gorge. At the end of the boycott in 619 AD, both Khadija and Abu Talib died due to increased weakness and advancing age. The Holy Prophet(ﷺ) was so grieved by these deaths that he declared the year 619 as the "Year of grief".