How do you achieve an efficiency of more than 1 bit per Hertz?
One way is for instance amplitude modulation. Imagine a system where the receiving end of a transmission pair is aligned and setup in such a way that the received waveform is always exactly proportionate to the sent waveform. The sending party now sends a carrier wave and modulates its amplitude at 1Hz, but it can send many different levels which can all be distinguished by the receiving end.

For instance, you can encode 4096 different levels even though the bandwidth is just one Hz. Each state contains 12 bits of information. Bandwidth is 1Hz. Voila.

Of course, in any real-world application there is noise, interference, not to mention the receiver is often moving with respect to the transmitter. It is hard to distinguish so many different signalling levels. How much can be distinguished is what we call signal-to-noise ratio (SNR), and this is why people say that with high enough SNR you can transmit more than 1 bit per Hz of bandwidth.

Besides amplitude modulation, phase modulation (using two carriers) is also used to transmit information. The arbitrary combination of these methods is called QAM or quadrature amplitude modulation. For instance, QAM-2048 is what my glass fiber internet connection uses, which means that each Hz of the carrier can convey 2048 levels or 11 bits of information.