What is the meaning of Acts 16:33?

33 And he took them the same hour of the night, and washed their stripes; and was baptized, he and all his, straightway. (Acts 16:33 KJV)

William Burkitt’s Commentary

Behold how sudden and strange a change was wrought in this gaoler. Before his conversion he was cruel, barbarous, and hard-hearted; now he is meek, merciful, and compassionate. He that before had beaten, imprisoned, and hurt the holy apostles’ feet in the stocks, now pities them, mourns over them, and washes their stripes.

Learn thence, That religion, and the grace of God, soften and mollify the hardest hearts, sweeten the sourest natures, and change the most barbarous and bloody dispositions. Behold this gaoler, before his conversion, a savage persecutor, a tiger, and a vulture, like the demoniac in the gospel, exceeding fierce: but now dispossessed of his fury, and by grace turned into a lamb for meekness, and a dove for innocency.

Observe, 2. How the gaoler believing, he and all his house were baptized. The apostle denied not baptism to the gaoler’s household, upon the gaoler’s sincere profession of the Christian faith; yet no doubt he promised to use his utmost endeavours to bring them to the knowledge and obedience of Jesus Christ.

Observe, lastly, How improbable it is that the gaoler and his household were baptized by dipping. We do not deny the lawfulness of baptizing by immersion; but we cannot assert the absolute and indispensable necessity of it. St. Paul, who was newly washed, and his sores dress, occasioned by stripes, cannot be supposed either to go out himself, or to carry the gaoler and all his family, in the dead of the night, to the river or a pond to baptize them; neither is it in the least probable, that St. Paul himself was baptized by dipping. He arose, and was baptized; and when he had received meat, he was strengthened. Ac 9:18-19

The context may convince us, that he was baptized in his lodgings, being sick and weak, having fasted three days, and being in a very low condition, partly by his miraculous vision, and partly by his extraordinary fasting: it was no ways probable that Ananias should carry him out to a river in that condition, to plunge him in cold water. Dipping, then surely, cannot be so essential unto baptism, as for want of it to pronounce the baptism of all the reformed churches throughout the world to be null and void, as some amongst us do.