There are two sources of the name Anderson: Scottish and Scandinavian. Both are derived from the Greek word Andreas, which means strong, manly or courageous.
In America today there are many Andersons (894,704), some of them still spelling their name Andersen, who were born in Sweden, Norway or Denmark. This article broadly outlines the great and famous Andersons, the ones who have walked the halls of Congress, thrived in business, written the books, preached from the pulpits and fought the wars. Statistically, "Anderson" is the the 12th most common surname in the United States.
Oddly, very little column space is devoted to the infamous Andersons (ie. Confederate thug "Bloody Bill" Anderson).
The most common last name in the English speaking world (except Canada) is "Smith" - read about it...