Answer:
A soliloquy has been described as a long speech expressing thoughts of a character alone on stage.
The best example of a soliloquy is Juliet's "Gallop apace, you fiery-footed steeds" at the beginning of Act 3 Scene 2. Or "Farewell! God knows when we shall meet again" in Act 4 Scene 3.
The balcony scene has Juliet speaking when she thinks she's alone, although Romeo is listening in. To most people that would also qualify as a soliloquy, even though Juliet is not alone on the stage. So would Hamlet's "To be or not to be" speech although he's not alone on the stage when he says that either.