Your last name is a vital clue to your past, but can also give clues about your present. In Western patriarchal societies, last names follow the male line down generation after generation. For this reason, you can look back through census records over centuries to see the countries that your last name moved through over time.
This chronicled journey allows you to look back to the base of your family tree and discover your origins. Did your family originate from the United Kingdom, France, or Germany? You can see that and more by signing up for services like Ancestry.com.
Additional to heritage and history, you last name also carries implications about you and your history:
You are able to see how long members of your family live on average in order to clue in on the effect that your genetics and inherited circumstances might play in your chances of becoming a centenarian.
Certain last names are more predisposed to certain occupations than others based on their long-time family trades and socio-economic classes. For example, the main occupation for the Rothschild family could be drinking martinis on the beach if they were so inclined.
Some last names were actually born out of the trades carried by your forefathers. In olden days, it was often efficient and economical to carry a last name of your profession like Smith, Goldsmith, Carpenter, etc.
Meanings have changed throughout the years though and certain names can indicate a diaspora out of a certain country and into another. For example, there were many misspellings of traditional names made at Ellis Island during immigration which have been traced and recorded. Some last names were even made up there in order to ease the immigration process.
You can look into campaign records and voting records in some locations to see the political persuasions of your family. You can even look up war records to see who served in previous world wars or even in the United States civil war.
Often the best details are the unexpected. There are troves of documents associated with your forefathers by their last names which can be found. These documents often provide the best insight into your family's history and can give detailed illustrations of the lives of your forefathers.