Surely means without doubt or certainly. When you say “Surely we'll finish the project on time,” you're expressing confidence that it will happen. When a teacher says “You surely know the answer to this,” she's indicating that she expects you to.

The word carries a sense of certainty, but it's softer than saying something is absolute. If your friend asks “Will it rain today?” and you look at the dark clouds and reply “Surely it will,” you're saying you're very confident, even if you can't guarantee it.

People also use surely to express surprise at something obvious. “Surely you're not going outside without a coat in this weather?” really means “I can't believe you would do something so clearly unwise.”

In British English, surely sometimes appears at the start of questions to challenge something that seems wrong: “Surely the library closes at 5:00, not 3:00?” The speaker believes 5:00 is correct and is questioning the other time.

One caution: the phrase “slowly but surely” means making steady progress even if it's gradual, like building a tall tower one block at a time.