I presume what you're talking about is digital sampling of an analogue signal?, as you've found out it's crucial to sample a fair bit faster than the maximum frequency in your analogue signal. To this end it's normal to have a low-pass filter before you're sampling.
It's quite easy to show why this is, all you need is a piece of graph paper.
OK - assuming you have a piece of graph paper 10 squares wide, draw a single sinewave across the entire 10 squares. Now read the value off of the vertical axis where the sinewave crosses each square - this will give you 10 vertical points. Now plot those points on another piece of graph paper, and join the points together with a line - it should give you an approximation of the original sinewave. Bear in mind, if doing this electronically, you would have another low-pass filter after you convert back from digital to analogue - this will tidy the sinewave somewhat.
Now do the same thing again - but instead of drawing one sine across the paper, draw more - try ten for a nice simple example. Take the readings and plot them again - and see what you get then!.
Then try different numbers of sinewaves, and see where it becomes totally unuseable!.
As a matter of interest, CD audio is sampled at 44.1KHz and has a maximum frequency of 20KHz - so that's sampling at only 2.2 times the maxmimum input - which is about as low as you can get away with.