When working with an Analog signal (like playing back tape) and running it through an effects box (say reverb) you are altering the sound "waves". Digital audio is stored as binary info, basicly a series of 0s and 1s. If you use a computer program to add (for example) reverb to a sound file on your computer, you are using math calculations to digitally duplicate what a effects box would have done. So if your original data is more presisely represented by a larger number of 0s and 1s, you can make more presise alterations to it.
Now having said that, I should admit that in my case I don't completely follow this advise. My hardware supports 24 bit, 48K recording. There is a LARGE and clearly audible difference in 16 vs 24 bit. However I could hear no clear difference in my test recording of 44.1 vs 48. Since everything has to ultimately go to 16 bit / 44.1, and since my program of choice does 24 to 16 but NOT 48 to 44 conversion, I record everything at 24 bit / 44.1 and then convert the final stereo master track to 16 bit.