Resample changes the sound's sample rate up or down. It uses a very high quality algorithm that has virtually no alias distortion or noise.
Sample Rate - The sample rate can be from 1000 to 1000000 hertz. The popup list has some of the most common sample rates.
Resample - If checked it will resample the sound, otherwise it will just change the sample rate.
Quality - Good, better, best or ultra. All of them are virtually alias distortion and noise free. They mainly differ by the steepness of the filter's slope. For example, "Ultra" has the steepest slope, but it is the slowest.
The highest frequency a sound can have is half of the sample rate. This is called the Nyquist frequency. So the highest frequency a 44100 hertz sound can have is 22050 hertz. Any frequencies higher then 22050 hertz (that aren't filter out) will cause alias distortion.
It will work as a low pass filter with a very steep slope if you don't change the sample rate and "Resample" is checked. "Quality" will control the steepness of the filter's slope.
You can see a comparison of many different sample rate converters here: