What does Acts 9:19 mean?

Saul has had his life completely turned around. Four days before, he was on his way to Damascus to arrest Jewish Jesus-followers and return them to Jerusalem for trial for their blasphemy. Now, he himself is a Jesus-follower. After meeting Christ on the road and temporarily going blind, he fasted and prayed for three days. Ananias arrived and baptized Saul, and the Holy Spirit came and filled him. He can see again; now he's hungry (Acts 9:1–18).

In the culture, to eat with someone is to affirm a fealty with them. When Saul accepted Jesus as his Lord and Savior, he was reconciled to God (Romans 5:10). His sins are forgiven, he has no more requirement to fulfill the Mosaic law. But he is also reconciled with other Jesus-followers, and he is on a mission to make more.

Saul's steps over the next few years are unclear. He does stay in Damascus for "some days," but after that, he apparently goes to Arabia and then returns to Damascus (Galatians 1:17). This probably doesn't mean the Arabian Peninsula, which is all desert; he may have just gone east of Damascus into the wilderness, or even toured some of the nearby towns. When he returns to Damascus, we know that he will barely escape from the Jewish leadership and then go to Jerusalem to meet the apostles. Unlike Ananias, however, it doesn't appear that Jesus warned Peter, John, and James that Saul is coming (Acts 9:20–30).