What does Matthew 14:5 mean?

Matthew is describing how John the Baptist came to be imprisoned and eventually killed by Herod the tetrarch, the Roman-appointed Jewish ruler of Galilee and Perea in Israel. Herod, also known as Herod Antipas, had divorced his wife and married his brother's wife. John the Baptist had called him out publicly, saying that this was in violation of Jewish religious law. For the sake of that wife, Herod had John arrested and imprisoned (Mark 6:14–19).

Likely to please his wife Herodias, Herod had initially wanted to have John executed. As a ruler, though, he had to be aware of how the people of Israel might respond to this action. It's not that Herod could be voted out of office, but his obligation under Roman rule was to maintain the peace in his region of Israel. He had the authority to arrest and execute anyone for nearly any reason, but he could not risk causing an uprising. Even if the people themselves didn't succeed, such unrest would have brought great trouble from the Roman government.

Many people thought John the Baptist was a prophet sent from God like the Israelite prophets of old. Some, including Jesus, said John was the fulfillment of God's promise to send Elijah again (Matthew 11:14). Herod was afraid to give the people reason to think that he was defying the will of God by killing His prophet. That fear was only temporary, however.