How superpositions and spooky action at a distance could help factor massive numbers...
...its state cannot be described without also referring to the state of another object or objects, because they have become intrinsically linked, or correlated.
No physical link is required however - entanglement can occur between objects that are separated in space, even miles apart - prompting Albert Einstein to famously dub it "spooky action at a distance".
The correlation between entangled objects might mean that if the spin state of two electrons is entangled, their spin states will be opposites - one will be up, one down. Entangled photons could also share opposing polarisation of their waveforms - one being horizontal, the other vertical, say. This shared state means that a change applied to one entangled object is instantly reflected by its correlated fellows - hence the massive parallel potential of a quantum computer.
With enough entangled qubits at its disposal, a quantum computer then becomes a vehicle for doing massive parallel processing or tackling hard mathematical problems such as factoring huge numbers - a task that classical computers struggle with.
Once an entangled state has been created between two objects, it is also possible to know the other object's state indirectly by measuring its entangled fellow.
It's a bit like taking a peek at someone's ankle and checking out one of their socks - once you've seen the repeating sheep pattern poking out of their shoe, you can be pretty sure you know what's on their other foot. In the quantum world, meanwhile, you can be absolutely sure of the state of one entangled object after peeking at its correlated fellow.
OK I kind of get the idea but what is it used for? What sort of practical applications does it have?
Entanglement has various applications and potential uses. Quantum cryptography, for instance, uses the phenomena to guarantee secure communication. Should an eavesdropper interact with an entangled object - that is, by intercepting and listening to it - it would alter its entangled fellow and thereby give away the spy's presence.
As a result, if the entangled object arrives unchanged at its destination, it's possible to know with absolute certainty that a communication has not been intercepted en route.
Another process that makes use of entanglement is quantum teleportation, which essentially enables information stored on a qubit to be transferred from one quantum system to another without physically transporting the qubit itself or broadcasting its contents (neither of which is physically possible).
Teleportation of the data, however, can be achieved between a sender and a receiver with a little sleight of hand by utilising the correlation between a pair of entangled qubits that the two parties share between them to calculate and then recreate the information at the destination point.
And, as mentioned above, entanglement is also essential...