Avdol and Jean both first met while Jean was under the control of DIO. Jean attempted to assassinate Avdol and the other Crusaders. He and Avdol fought each other, and Avdol respected his bravery and his honor. After it was shown that Jean was under the control of DIO, and Jotaro managed to free him, they became friendlier with each other, although they fought and argued a lot. During the fight against Hol Horse and J. Geil, Jean acted recklessly, attempting to kill them both, and nearly dying. Avdol jumped in front off him and "died". Upon realizing that Avdol was "dead", Jean began to cry, realizing how important Avdol was to him.
Polnareff meets Cameo's Judgement, who says that he can make Jean's three wishes come true. One of Polnareff's wishes is to bring Avdol to life, as he thought that Avdol was dead, and hoped that this would bring him back to life. However, Jean was tricked. Judgment didn't actually bring Avdol back to life, but rather a clay construct of Avdol. As Jean was about to die, the real Avdol appeared and saved him. When Jean sees the real Avdol, and Avdol saves him, Polnareff cries again, but this time, he cries tears of joy. From this moment forward, the two become good friends, and work together more.
In the last episodes of Stardust Crusaders, Avdol really dies in the DIO's mansion. After defeating Vanilla Ice, Jean sees Muhammad's and Iggy's ghosts. After this, Jean tells himself there's no time to cry. However, because Avdol (and Iggy) were very important to him, he begins to cry over the loss of his friends.
Avpol isn't a very popular ship in the JoJo fandom, but it's the second most popular ship from Stardust Crusaders, coming after JotaKak. Many shippers enjoy their dynamic.