What does Matthew 14:13 mean?

What did Jesus hear that prompted Him to withdraw to a desolate place? Merely starting at the previous verse might suggest He was responding to the death of John the Baptist, as reported by John's disciples. However, Matthew began this chapter with Herod's remarks on Jesus' fame and power, which he associated with John the Baptist. What follows was the backstory about John's death. Now Matthew seems to pick up where verse 2 left off. In short, the "this" which Jesus is hearing about seems to be Herod's notice, not the death of John.

Jesus lived and ministered in the territory under the rule of Herod Antipas, who had been manipulated into killing John (Matthew 14:3–12). It was probably Herod's attention which motivated Jesus to move away from busy Capernaum to a sparsely populated area. The disciples remained with Jesus; He was by Himself in the sense that He was away from the crowds of people that constantly followed Him. He wouldn't be away from them for long, however.

We know from the same account in Luke that the lonely place Jesus headed for was Bethsaida (Luke 9:10). It was on the northeast shore of the Sea of Galilee. The crowds of people, though, figured out where Jesus and the disciples were headed. As they travelled by boat, the crowds ran along the shore of the lake from Capernaum up and over the Jordan river and down to Bethsaida. When Jesus arrived for some alone time with the disciples, He found the crowds waiting for Him.