Quantum computers would offer two advantages: - Extremely fast calculations for certain types of problems, such as the problem of protein folding which means in this case the ability to discover new drugs and cure diseases much faster. - Much more secure systems, since modern cryptography is mostly based on multiplying large numbers and factorization of numbers (the opposite operation of multiplication, i.e. finding the original factors that were multiplied). Quantum computers would be able to do this much faster with much larger numbers.
The reason the technology is not ready yet, is that several techniques and functionalities of classical computing have not yet been reproduced in Quantum Computing, or they have been but they're not yet efficient or scalable, which is what researchers are trying to mend. These techniques for example include short and long term memory, fast calculations, data transmission, etc. The article you linked basically talks about a research attempt to implement data transmission between quantum systems using a phenomenon called "entanglement". It's considered a breakthrough mainly because of the distance. The proof of concept had already been established, and the issue is now just scaling to larger, hence more useful, systems.
It's unlikely however that you'll ever have a Quantum Computer at home. Preserving Quantum memory bits (called qubits) requires delicate conditions to avoid any unwanted interactions that would cause decoherence (qubits losing their quantum state, thus their memory content). This can only be achieved in the lab. So, if useful Quantum Computers one day come to light, they will likely be confined to data centers, and their effect on society would mostly be felt through their scientific and technological applications.
Initially, quantum computers will make all modern forms of encryption MUCH LESS secure - because the first organisations to get quantum computers will be able to decrypt all existing messages (and past ones, if they recorded them) in a trivial amount of time.
Some people (conspiracy theorists?) believe that some government agencies and/or large tech companies already possess this technology, or that they soon will, and that whenever they get/got it they will try to keep it secret for as long as they can - during which time they can spy on everyone.
If and when quantum computers and especially quantum communications networks become generally available, then it will allow everyone to use perfectly secure communication - which many governments won't like.