If someone intercepts the quantum key, it will modify it 25% of the time. If you randomly measure (and verify publicly with the sender) a fraction of your total key and find it unmodified, it means the rest of the key probably is too, up to a certain security factor. By starting with a longer key and measuring more of it (or doing privacy amplification, for example xor-ing multiple keys together), you can get as much security as you want. It also means the security is everlasting, meaning someone cannot retroactively break your key in 100 years using some mega-computer.