This depends on the surname, as different surnames have different origins, but a great many surnames originate as indicating (a) familial lineage, (b) place of origin, (c) profession, or sometimes (d) a physical characteristic.
Professions are the easiest: John Smith originates as, literally, John the smith; smithing was his profession. Fisher, Tailor, Weaver, Miller, Carpenter, Shoemaker, etc. all have the same origins.
Parental lineage is also obvious in some contexts: Bill Johnson = "Bill, son of John". Similarly, Bill O'Brian = "Bill of Brian", meaning "Bill, son of Brian". MacDonald = "son of Donald", D'Antonio = "son of Antonio", Rodriguez = "son of Rodrigo", and my favorite: the weighlifter Magnus ver Magnusson's name literally means "Magnus, son of the son of Magnus"
And since O', Mc, Mac, D', De, ver, von, -uez, and many others all mean "of" or "from", they can also be used to indicate a place they are from rather than a parent. Leonardo Da Vinci, for instance, means "Leonardo of Vinci", because he was literally from the town of Vinci.
Physical characteristics aren't as common, but still, there are plenty. The Slavic name "Plesko", for instance, means "bald", so Steve Plesko = "Steve the bald".
First of all, last names are not universal. There are entire cultures where the idea of a single surname passed down from father to children over generations is either the exception or unknown. In Iceland, for example, people have second names but they don't usually use them, and the second name is individual, not familial: Thor Magnússon's son might be legally named Carl Thorssen and his daughter Helgú Thorsdottir, but even formally the children would be known only as Carl and Helgú unless there was a need to differentiate them from another Carl or Helgú.
Western surnames can be classified in many (oh so many) ways, but I like to break them down into five large categories depending on what they're based on:
That all said, names aren't set in stone. They change over the generations. Mitt Romney is a good example; seven generations back the family surname was Rumley. In Scotland and Ireland, whether a family is a "Mac" or a "Mc" has more to do with the preference of the (often English) official who first wrote the name down than anything else; there are cases where one brother is a Mc, the next is a Mac, the third is a Mag, and a cousin is a M'!
hi! you'll find more examples in the FAQ