For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
God: Elijah why are you hiding in this cave?
Elijah: It's just me against the world!
God: I think you've forgotten how I work...
God wasn't in the strong wind, the earthquake, nor the consuming fire. He reminded Elijah that he had been hearing from God as a 'Low Whisper.' (emphasis mine).
In short, Elijah was saying 'I'm tired!' God told him, 'I have many others who will succeed you.' (1 Kings 19:18).
Then God told him who he was to go and anoint as God's new team; he was going to be relieved of duty. He was to anoint Hazael to be king of Syria, Jehu to be king of Israel, and Elisha was to replace Elijah as prophet.
Elijah didn't have to worry about Ahab and Jezebel anymore, their reign was finally over. That's what God meant by telling him to go and anoint these others to take over.