What does Acts 5:37 mean?

When Peter and John preached that Jesus of Nazareth had risen from the dead and proved their authority by performing miracles through His power and authority, the priests were perturbed. Most of the priests were Sadducees, a Jewish sect that didn't believe in the resurrection of the dead. They warned Peter and John to stop teaching about Jesus but had to let them go as they hadn't technically broken any laws (Acts 4:1–22).

Shortly after, the priests find all the apostles preaching about Jesus in the temple courtyard. When they question the men, Peter insists that this Jesus, whom the priests and other members of the Sanhedrin had killed, is the Jewish Messiah and now sits at God's right hand (Acts 5:30–32). What had been a matter of jealousy (Acts 5:17) is now a trial of blasphemy.

Gamaliel is a highly-respected Pharisee who does believe in the resurrection of the dead, but doesn't like Jesus or His followers. He attempts to calm the apoplectic Sadducees. He mentions two previous troublemakers, Theudas (Acts 5:36) and Judas the Galilean, as examples. His main point is that if God doesn't support a spiritual movement, God will defeat it. That's not necessarily true in the simplest sense—God has sometimes allowed false teaching and evil to persist before bringing judgment, as can be seen by the many world religions prevalent today and even false teaching within Christianity—but as a general rule of thumb, it works. Movements that are not of God, especially within Christianity, tend to die out relatively quickly.

We don't know anything about the Theudas mentioned by Gamaliel, but there is historical information about Judas the Galilean.

Gamaliel mentions that Judas gathered his following "in the days of the census." The only census of note is that of Quirinius at the time of Jesus' birth (Luke 2:1–3). Josephus mentions that Judas was from the territory on the eastern shore of the Sea of Galilee. While he may not have been from the district of Galilee, he was from the area around the Sea. Scholars also say that although he was killed and his people scattered, his followers regrouped. That remnant became the Zealots: fiercely anti-Roman and not opposed to violence. Although they are not especially active at the time Gamaliel speaks, in AD 66 Zealots will cause a rebellion that will result in the Roman army razing Jerusalem and burning the temple.

So, Gamaliel is correct, albeit in a way he didn't intend. Theudas came to nothing. The followers of Judas the Galilean, however, will cause the destruction of Jerusalem and the temple (Hebrews 8:13). In a strangely parallel way, Jesus' message negates the importance of both the city and the architectural center of Judaism. Stephen's entire pre-martyrdom defense explains how God cannot be contained in the temple, and neither can His worship (Acts 7:44–50). Paul spreads Christianity throughout the Roman Empire, proving the worship of God isn't confined to a geographic location. The followers of Judas the Galilean inadvertently prove the point of the message of the followers of Jesus. As Jesus told the Samaritan woman, God doesn't need a building. "True worshipers will worship the Father in spirit and truth" (John 4:23).