Surname Meanings
In the small communities of our distant ancestors, surnames or family names were not commonly used. The concept just wasn't necessary when everyone knew everyone else. But as villages grew into larger towns and people started travelling farther from their homesteads, the custom of having a family name took hold.
Many older surnames began as simple descriptors of a person. They may have reflected an occupation, birthplace, appearance or other quality. These crude names weren't true surnames as they weren't passed on through the family. Each name was associated with a single person only.
Another form of surname is the family name, where a person identifies himself as being related to his father (usually). This form of naming was common in Scandinavian and Celtic countries. Yuri Bjornson would have been Yuri son of Bjorn.
Other patronymic (father-based) names that we still see today come from the Gaelic (Mac, Mc), Norman (Fitz), Irish (O') and Welsh (ap). But even these family names weren't consistent through the generations, as each new son would have a new last name.
Some online databases with meanings and origins of last names can be found here:
Given the vast number of surnames in use today, most websites don't do the subject justice in their scope. You might find it worthwhile to invest in an actual book on surname meanings.
Here are a few that I found, that you could purchase online. Any one of these books could be a valuable addition to your genealogy library.