"Safe and sound" means completely safe, as Gary said. For example, you could say "I arrived home safe and sound." Or, if a friend texts you, "did you get home okay?" you could reply with "yep, safe and sound!"

It is actually "saFe and sound". It basically means safe. It's similar to how Chinese often uses two words with similar meanings as a phrase to reinforce the meaning. 'Sound' when used in this way means solid and undamaged. The boat's hull appeared sound. His reasoning was sound.