What does Acts 10:31 mean?

Cornelius, a Roman centurion stationed in Caesarea Maritima, is explaining to Peter why he asked the apostle to visit him. He is recounting how a few days before, an angel appeared to him.

In Acts 10:4, the angel says, "Your prayers and your alms have ascended as a memorial before God." The memorial offering is the part of a larger offering that is burned when the rest is given to the priests (Leviticus 2:2–3). Eating together is very important in the culture—Jewish and Gentile. To eat with someone is to publicly identify with them, which is why the Pharisees were shocked to see Jesus eating with tax collectors and "sinners" (Mark 2:13–17).

When the priests burned a "memorial offering," they in effect shared a meal with God. God counts Cornelius' prayers and alms, meaning charitable giving, as the memorial portion of an offering. Peter may remember that Jesus spoke of this. He said that if anyone gives a drink to the thirsty or houses the foreigner or visits the sick, it is if they did so to God. Peter must be surprised to realize God considered Cornelius' giving the equivalent to eating a meal together.

The day after Cornelius' visit with the angel, Peter had been on a rooftop, receiving his own vision. In it, God told Peter that the restrictions on food were lifted. Peter is beginning to understand that if any food is fit to eat, then any person must be fit to eat with—even a Gentile. Soon, he will see that God accepts any person into His fellowship through Jesus Christ (Acts 10:44).