At this point, we've caught up to the time period of the main events of the story. Alyosha (a nickname for Alexei) is now 20, Ivan is 24, and Dmitri is 28. Of all the sons, Alyosha is least like Fyodor. He's pure, sweet, and everyone spontaneously loves him.
Alyosha had initially come to town to visit his mother's grave. Just three years before, his father had gone off to Odessa and made a pile of cash. Upon his return to town, he devoted all his time to acting like a fool and humiliating women and generally creating scandal.
Fyodor didn't even remember where Alyosha's mother was buried – Grigory the servant had to show Alyosha the grave marker. After seeing his mother's grave, Alyosha asked his father's consent to enter the monastery, and after cracking a few blasphemous jokes, his father consented.