What does Acts 12:21 mean?

Not even Josephus seems to record the connection between Agrippa's speech and his argument with Tyre and Sidon. Antiquities 19.8.2 343–361 does give more information regarding the setting, however.

Agrippa is in Caesarea Maritima, the Roman capital of the region on the coast of Samaria. It is the second morning of the games he has inaugurated in honor of Caesar. He is wearing garments made of silver, and when the morning sun falls on him, he glows. Some think he intends to emulate the Phoenician sun god, while others think he just likes how it looks. When the people see him, they say, "The voice of a god, and not of a man!" (Acts 12:22).

Normally, Agrippa has a measure of respect for the Jewish God. On this day, he delays rebuking the people's blasphemy and God responds. Perhaps because he is a public leader who claims to follow God, an angel strikes him (Acts 12:23), and he gets a terrible pain in his gut. Josephus says he also sees an owl—a harbinger of death. Agrippa, according to Josephus, spent the next five days in agony before he dies, his bowels eaten by worms.

"Throne" is taken from the Greek root word bema. It's a throne in that it's the seat of a king, but specifically it's the raised platform where a king sits when he makes a judgment. It is also translated tribunal (Acts 18:17; 25:6, 10, 17). When Jesus-followers are judged, it will be before the Bema Seat of Christ where He will reward us for our obedience to God (Romans 14:10–12; 2 Corinthians 5:10).