The well of Zamzam had been buried and lost since the Khuza'a-Jurhum wars generations earlier, forcing the people of Makkah to fetch water from outside the valley. Abdul Muttalib saw a dream, repeated several times, instructing him to dig between two idols by the Ka'bah to find it. With only his eldest son Harith to help him (his other sons were not yet born), he took a shovel and axe and dug until he struck water, to the mockery of the Quraysh who did not believe he would succeed. When the water appeared, his relatives claimed a share of the rights, and the dispute nearly came to blows. Abdul Muttalib refused, and it was in this dispute that he vowed to Allah that if he were given ten sons to defend him, he would sacrifice one of them. The two sides agreed to consult a priestess, but on the journey the party nearly died of thirst; as Abdul Muttalib dug his own grave (as they all did, being too weak to bury one another), water sprang up again, which the Quraysh took as a sign from Allah confirming Zamzam belonged to Abdul Muttalib, and they turned back without going to the priestess.
Outcome: Zamzam's rights were confirmed to Abdul Muttalib without recourse to the priestess, after a second, unrelated spring of water appeared during the journey to consult her.
Restored the pilgrims' water supply and gave Abdul Muttalib and his descendants custody of Zamzam, adding to the prestige that would descend to the Prophet Muhammad ﷺ. It was also the occasion of Abdul Muttalib's vow concerning one of his sons.
No. I discovered it. I have the rights.
Said when his relatives surrounded the newly-uncovered well of Zamzam and claimed a share of it as tribal property.
Each one of you should dig his own grave, for we are too weak to bury each other.
Said to his companions when the party journeying to consult a priestess nearly died of thirst.