Abdu’l-Muttalib was the grandfather of the prophet
Muhammad. His name breaks down into two parts:
Abd, which means servant, which is one of the reasons why Abdullah (abd-Allah) is a very popular name for muslims.
Al-Muttalib was the uncle of Abdu'l-Muttalib.
According to the history of the Arabs Abdu’l-Muttalib's father, Hashim, died when Abdu’l-Muttalib was very young. His mother was from a very noble and wealthy clan so after her husband died she returned to her parents. Since they were from a wealthy clan her son had all of his desires fulfilled and had a very comfortable life.
When Abdu’l-Muttalib matured Muttalib felt that Abdu’l-Muttalib should return to the clan of Quraish. Muttalib felt since the Quraish, being the care takers of the kabah, were a very respectable clan that Abdu’l-Muttalib should return to Mecca. So Muttalib went to his sister-in-law and asked her to return the boy to him. She told Muttalib to ask the boy. She said something to the effect of:
"If he wants to go with you, he has the right. I will give him the freedom to go with you. If he wants to stay with me, I am not going to force him to go with you."
When they asked the boy, he said that he would like to go with his uncle Muttalib. When Al-Muttalib returned to Mecca with his nephew riding on the back of his camel people thought that he had bought a boy as servant, which was normal for those days. So from that time on they started calling him Abdu’l-Muttalib.