In Acts 16, when Luke reports on the conversion of two locals (a wealthy merchant named Lydia and a jailer), he tells us that Paul baptized their entire households. Why would Paul baptize an entire household?
Background
Paul made 3 major missionary journeys. He first visited the Macedonian town of Philippi on his second journey which is recorded in Acts 16. Typically, when Paul entered a new city, he went to the synagogue on the Sabbath and proclaimed the gospel. Since he do not go to a synagogue, we can presume there was none. Instead Paul went to a place by the river where some women gathered to pray.
Lydia's Conversion
16:13And on the Sabbath day we went outside the gate to the riverside, where we supposed there was a place of prayer, and we sat down and spoke to the women who had come together. 14One who heard us was a woman named Lydia, from the city of Thyatira, a seller of purple goods, who was a worshiper of God. The Lord opened her heart to pay attention to what was said by Paul. 15and after she was baptized, and her household as well, she urged us, saying, "If you have judged me to be faithful to the Lord, come to my house and stay." And she prevailed upon us. -Acts 16:13-15 ESV
The Jailer's Conversion
Paul has been arrested, beaten and thrown in prison. During the night, an earthquake opens the doors of the jail. When the jailer realized, the prisoners all remained inside, he rushed into their cell.
16:25About midnight Paul and Silas were praying and singing hymns to God, and the prisoners were listening to them, 26and suddenly there was a great earthquake, so that the foundations of the prison were shaken. And immediately all the doors were opened, and everyone's bonds were unfastened. 27When the jailer woke and saw that the prison doors were open, he drew his sword and was about to kill himself, supposing that the prisoners had escaped. 28But Paul cried with a loud voice, "Do not harm yourself, for we are all here." 29And the jailer called for lights and rushed in, and trembling with fear he fell down before Paul and Silas. 30Then he brought them out and said, "Sirs, what must I do to be saved?" 31And they said, "Believe in the Lord Jesus, and you will be saved, you and your household." 32And they spoke the word of the Lord to him and to all who were in his house. 33And he took them the same hour of the night and washed their wounds; and he was baptized at once, he and all his family. 34Then he brought them up into his house and set food before them. And he rejoiced along with his entire household that he had believed in God. - Acts 16:25-34 ESV
Infant Baptism
Many denominations practice baptizing their infants as a sign of the covenant and Acts 16 is one of the places they use to support the practice. I'm not going to discuss the issue of infant baptism. If you're interested in that, please read the debate on infant baptism between John MacArthur and RC Sproul.
Instead I want to look at this issue of baptizing a household from a Bible study standpoint only. What clues do we have in the text that might help us figure out what is going on - regardless of its theological applications?
Who made the decision?
Chapter 16 is the first time in Acts that baptizing the whole household is mentioned. That suggests it may not have been a common practice.