Resolution in an audio file is similar in some ways to thinking about resolution in a digital image.
In Photoshop if you have more pixels in an image it is rendered more accurately:
In audio, the waveforms and the fidelity of the sound are also impacted by the amount of digital information in the file. There are two measurements of resolution: Sample Rate and Bit Depth.
Sample Rate:
The most common sample rate, and the standard for most CDs Mp3s, etc. is 44.1kHz. Many cameras (for example Digital SLR cameras) record and 48kHz. Most decent audio recorders allow you to choose the Sample Rate before you record.
Here is some information about Sample Rate from the website The Hub
“digitized audio is a series of “snapshots” that we hear as continuous sound. How often these audio snapshots are taken is referred to as the sample rate. The more snapshots taken, the more detail the sound has. These pictures illustrate how sampling works”
These are exaggerated examples, but helpful. The wave in Figure 1 is 1 second long. Figure 2 shows a sampling rate of 5, (that’s 5 samples a second) Figure 4 shows a sampling rate of 10. Notice that the fidelity of the wave gets a little better?
Now imagine the standard sample rate of 44.1kHz , that’s 44,100 of those samples in a second! The increased resolution means a better frequency response.
Bit Depth:
Here is some information about Bit Depth from the website The Hub
“The other part of the digital audio equation is bit depth. Much like the sample rate defines the frequency response as it divides up the horizontal axis of the waveform, the bit depth defines the dynamic range of the sound as it describes the amplitude of the waveform at each sample point. 8-bit audio gives you 256 separate levels for each sample. 16-bit audio gives you up to 65,536 levels, and 24-bit samples give you 16.7 million different levels! Let’s look at this a little more simply:”
Figure 7 has twice the sample rate described in Figure 4, yet the waveform looks more like a brick wall than a sine wave! That’s because the low bit depth offers very little in terms of dynamic resolution. The higher bit depth shown in Figure 7 results in significantly improved waveform resolution.
Here’s a video explanation
Here is a video tutorial that uses Adobe Audition to explain Sample Rate.