The Gospel of John is set entirely in the Roman province of Judea sometime between the years 28 and 33 CE (source, p. xxxviii). Who cares? Well, Jesus and his disciples lived and worked right smack in the middle of what are disputed Israeli and Palestinian territories today. Sadly, not much has changed since the 1st century: the people back then were pretty frustrated with their living situation, too.
This gospel calls out three key regions within the province.
The action of the story mainly alternates between Judea and Galilee. And, naturally, Jesus runs into different types of issues in both places.
The people of Judea were mostly Jewish and had been conquered and occupied by the mighty Roman Empire. This was no big deal to Rome—they had more important things to worry about than some insignificant Jewish province—but it was a huge issue for the people of Judea.
Many of them resented Roman rule. After all, the Romans had complete control over the land, laws, and government, and forced everyone to pay tons in taxes. The Jews were hoping (and praying) that God would send a messiah or "anointed one" to reclaim Jewish rule of Judea and to kick out the Roman occupiers.
Back home in Galilee, people aren't impressed with Jesus. Think about it, if the kid who grew up down the street from you starting telling people he was God's son, you would be skeptical, too. (That guy says he's sent from God? I knew him when he used to eat paste in kindergarten!) So when he's in Galilee, Jesus isn't exactly treated like a hometown hero.
In Judea, he has another problem all together: he seems to reek of Galilean wherever he goes. The people refuse to believe he's the messiah because he was born in Galilee. The messiah is supposed to be born in Bethlehem (which is in Judea.) That's probably why Matthew and Luke go through such trouble to get Mary and Joseph to Bethlehem for Jesus's birth. The Gospel of John, though, doesn't seem to care much about all that. The messiah was born in Galilee and the people will just have to deal with it.
Jesus is also usually in terrible danger whenever he's in Judea—especially Jerusalem. Though the religious authorities don't really like him in Galilee, it's the guys in Judea who are really gunning for him. They finally succeed when they turn him over to Pontius Pilate, who actually was the Roman governor of Judea during the time.
Lucky for us, what happened in Judea did not stay in Judea.