A means of transmitting an encryption key in a way that guarantees no evesdropping.
Quantum cryptography can guarantee there were no evesdroppers because it transmits the key as a series of photons (hence the “quantum” part). And photons, as Heisenberg tells us, cannot be observed without altering them.
Therefore, any attempt to evesdrop on the exchange of the key will corrupt it and make it useless.
So if two parties - Alice and Bob - want to exchange a message, then Alice could begin generating randomly polarized photons (each representing a bit) and send them to Bob. Bob then encrypts the message using the value of those photons as the key and sends it to Alice, but first he verifies with Alice that key was uncompromised with a method that cannot be used by Eve to deduce anything useful (like a checksum or, in practice, a report of the positions in a stream of photons where Bob's randomly polarized receiver was in “agreement” with the polarization of the photon Alice was transmitting). If the key was intercepted on the way by Eve, then the act of doing so would alter the key and the checksum of Bob's copy wouldn't match Alice's. So if the checksum didn't match, then they could keep trying new keys until Eve gave up.
The message, once a “safe” key has been confirmed, is uncrackable as long as the photons were sufficiently random.
A variation of quantum cryptography is to use entanglement instead. Entanglement is a phenomena where observing the spin of one particle will set the spin of its entangled cousin—no matter how great the distance they've been separated by (and instantaneously, too, defying the limit of the speed of light). In this case, Eve has no information to intercept because the value of the entangled particle hasn't been set until it has arrived at its destination and been observed.
The major barrier against implementing Quantum cryptography is the fact that it's bloody hard to transmit a photon, entangled or not, over great distances without losing it. If line-of-sight was not possible, then you'd be forced to use a pure fiber-optic end-to-end network between Alice and Bob—a non-trivial engineering task, since even high-quality optics need boosters every 15 to 20 miles (the act of boosting will change the photons).
