The phrase "safe and sound" is usually used when we talk about the end of a trip: e.g., We arrived home safe and sound.
Sound is a noun, verb, and adjective.
In the phrase "safe and sound" sound is an adjective and it means: "healthy, in good condition, free from injury, no damage, no accidents."
The adjective 'sound' also has other similar uses:
1. no defect, no disease, etc.; in good condition; healthy; robust: e.g., a sound heart; a sound mind.
2. financially strong, secure, or reliable: e.g., a sound business; sound investments.
3. competent, sensible, or valid: e.g., sound judgment, sound decision.
4. truthful, wise or reasonable: e.g., sound advice, sound recommendation, sound plan.