So basically it's quantum physics applied on computer science.
Computers of today are based on semiconductors and diodes, which allows us to build electric circuits with memory. In this case, it's voltage applied or voltage off - one or zero.
Quantum computing is a whole new world of computing; because it's based on the principles of quantum physics. This means that a quantum computer does not resemble the computers of today at all. In a quantum computer, information is stored in "qubits", which is 0, 1 or "undetermined / both". This is a direct application of the wave/particle duality of matter (wiki: De Broglie-wavelength). Working out how a quantum computer - which behaves totally differently from anything we have today - and constructing such a device is really hard. Theoretically, such devices would be more efficient than our computers - and that's an understatement.
This story means that we've taken yet another small step towards practical quantum computers, but also that it'll be reposted at least 100 times before working quantum computers are reality.
(Off the top of my head, please correct me if I wrote something in error. Thanks! :)