What does it mean to sweep someone off their feet?

It means that you've really impressed someone or you've greatly exceeded their expectations.

Example: I put a lot of thought in to her Christmas present and it paid off. That diamond necklace really swept her off her feet.
It can have two meanings the first one is where someone is kissing someone & they are picked up so they are swept off their feet by the person picling them up.

The second meaning is when someone falls for another person in a romantic sense & they are completely blown away. This could be someone who they have only just met or a person they have known for a while & they have now seen them in a whole new light.