There is no world without Verona walls
But purgatory, torture, hell itself.
Hence “banishèd” is banished from the world,
And world’s exile is death. Then “banishèd,”
Is death mistermed. Calling death “banishment,”
Thou cutt’st my head off with a golden ax
And smilest upon the stroke that murders me.

After being informed by Friar Lawrence that the Prince has exiled him for killing Tybalt, Romeo makes this graphic speech to convey that he would find the world outside the walls of Verona (in his words) “purgatory, torture, and hell.” It is safe to assume that this is due to his intense love for Juliet (of whom he will say, “Heaven is here / Where Juliet lives” later in the scene) and not due to any particular attachment to his home city. Read more about this quote in Quotes by Setting: Verona (the fifth quote).

I’ll give thee armor to keep off that word—
Adversity’s sweet milk, philosophy—
To comfort thee though thou art banishèd.

Friar Lawrence offers these words promoting philosophy as a relief to assuage Romeo after he learns of his banishment from Verona (and Juliet) in Act 3, Scene 3. Romeo’s response (“Hang up philosophy! / Unless philosophy can make a Juliet”) shows just how different these two men are. Friar Lawrence is a cultured and rational man, but it is safe to assume that he has never experienced a love anything like Romeo’s passion for Juliet.