Any sound that is digitised, i.e. any sounds on your PC, CDs, DVDs etc. have to be converted into a digital format as opposed to a single analogue wave. This means if you "zoom in" and look at a digital sounds waveform you'll notice that its not a smooth waveform but rather a series of tiny right angled "steps".
So the sample rates are just the frequency that these "steps" occur - the higher the sample rate, the more and smaller the steps are... which means more audio data, better quality, which = bigger file size.
Although unless you are a professional producer its not something you should really worry about - 44,100 should be fine (the same as CD audio).