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Too much wear (or too cheap a fabric), and a sweater's knit fibers come loose, bunching up and gathering in spots. This unsightly look is known as "pilling."
Many take this predicament as a sign the sweater has reached the end of its lifespan - but fear not, there is a solution!
A "sweater stone" is a small block of volcanic pumice rock, which you can find at major retailers and on Amazon for about $10.
Amazon.com
All you have to do to use it is lay your garment on a flat surface and brush the stone along the afflicted areas. The pills will fall right off.
Be warned: The sweater stone can sometimes leave some surfaces fuzzy, and since you are literally removing part of the sweater, it definitely won't increase its longevity or durability.