The basic idea is that all our computing efforts (to date) revolve around bits, a term which is actually short for binary digits. A bit can be on or off, 1 or 0. Inside the computer, bits are usually represented by electrical charges or currents, in an optical computer by flashes of light. But whatever the physical implementation, it still represents these binary quantities, that have just two possible states.

But suppose we could use quantum-level particles to represent bits? In the quantum world, you don't have just two states, you actually have three - on, off, and superposition. These new bits are called qubits, to distinguish them from the regular ones. It doesn't sound that useful, but having three possible states changes the basic logic that you can use, and means you can develop different sorts of algorithms, that turn out to be very powerful. A quantum computer can tackle problems that are just physically impossible to do with a regular computer, because it can do them so much faster (because the algorithms are so much more efficient).

Except that it's all pretty much theoretical, so far. Actually isolating and taming particles so that you can use them as qubits is very difficult, as you say. So while theoreticians have been thinking about what we might be able to do with a quantum computer, actually doing anything has been wishful thinking, since we are lacking actual physically real quantum computers. But people are trying to make them real.

Which is why this story is exciting. It's about an actual quantum computer tackling an actual real calculation. We seem to be at the cusp, moving from the theoretical to the practical. History in the making.