What does it mean to continue in the grace of God?
Acts 13:43 (ESV)
43And after the meeting of the synagogue broke up, many Jews and devout converts to Judaism followed Paul and Barnabas, who, as they spoke with them, urged them to continue in the grace of God.
In context, to continue in the grace of God suggests continued submission to the instruction of Paul and Barnabas regarding Jesus. It is to receive with faith what God has revealed and to shape your life accordingly.
43 And after the meeting of the synagogue broke up, many Jews and devout converts to Judaism followed Paul and Barnabas, who, as they spoke with them, urged them to continue in the grace of God.