XeononMan is essentially correct. There are a number of factors here.

The two processes going on in audio systems are: Analog to Digital conversion (ADCs or A/D) and then Digital to Analog conversion (DACs or D/A). Digital media, which is pretty much everything now, has already undergone the A/D process, which leave our processors to do the D/A conversion.

BITS
More Bits is usually better as the number of bits is directly proportional to Signal-to-Noise ratio (SNR) for the A/D conversion process. Each bit in the A/D adds approximately 6 dB to the achievable SNR of the sampled system (e.g. 24 bit A/D has a theoretical SNR around 144 dB) .

The rule of thumb for DACs is that you should have at least 2 more bits of accuracy in the D/A process than in your digital stream. Why? A well designed DAC typically has errors of +/- 2-4 LSBs (Least Significant Bits). By using a DAC with a couple more bits than your data you can feel pretty confortable that you DAC isn't adding noise.

Sampling Frequency
Higher sampling frequencies help too. As noted the highest frequency representable in the digital data is 1/2 the sampling frequency. The bad news is that any frequencies above 1/2 the sampling frequency fold back into the band of interest unless they are filtered out. This is called aliasing. With lower sampling frequencies you need a very sharp filter to minimize aliasing.

The process works in reverse on the D/A (DAC) side. The DAC creates an analog stepped waveform with frequencies up to half the reconstruction frequency and it needs to be filtered in order to recover the pure analog that we want to hear. Lower frequency DACs require steep filters.

Digital Processing
The third thing going on (I lied when I said two) is the digital processing which is such a huge topic that I'm not really going to go into it. I'll just say this: Digital processing can actually increase the sampling frequency and resolution (# of bit) of the original sampled data which can result in a higher fidelity signal than that recorded IF DONE PROPERLY. This doesn't create new data, you still have what was receorded, but it allows some more advanced processing to remove noise.

Bottom Line: It is possible to start with 24/44.1k bit data and process it up to 32/192k preserving the music and decreasing the noise.

Beware the Specs
The magic is still in the design and execution though. A bad design can make a 32 bit DAC perform worse than a well designed 24 bit DAC. Forget all the theory and let your ears decide.