What does Mark 7:31 mean?

Tyre was originally an island city off the coast of the Mediterranean Sea about thirty-four miles northeast of Capernaum. Sidon is also on the coast, about twenty miles north of Tyre. The text doesn't say that Jesus entered into the cities, just that He went into the region of which Tyre and Sidon were significant population centers. Tyre and Sidon are inhabited by Hellenized (Greek-cultured) Canaanites. The area is administered by Syria in service to the Roman Empire. The region is also called "Syrophoenicia"—"Syro" because of its ties to Syria, and "Phoenicia" for the purple dye the residents collected from murex sea snails.

Decapolis, by contrast, is east of Capernaum, on the other side of the Sea of Galilee. The northwestern arm borders the southeastern shore of the Sea of Galilee and the eastern shore of part of the Jordan River. The body of the district lies yet further east. "Deca" means ten and "polis" refers to cities. The cities referred to are actually city-states which share a similar culture but are administratively independent of each other.

Jesus apparently designs this circuitous route to avoid the district of Galilee. Their exact location in Decapolis isn't given, and neither is the particular shore on which Jesus earlier rescued the man possessed by a legion of demons (Mark 5:1–13), but they are in the same area. The last time He had been in Decapolis, the crowd had begged Him to go, but He told the man to tell his friends what God had done for him (Mark 5:14–20). Apparently the man's testimony acts as a sort of target-softening, and this time the people are much more receptive.