There was a time in the British Isles that people lived in small enough groups that everyone was identified only by a first name; John, William, Roger, Blythe; it was like a world full of Chers.
Eventually, the Isles became populated enough that confusion was often led to. Bruce, the man covered in pig feces speaking to you know as he takes a break from his feces gathering duties, describes how drunk he and Dwyght became after drinking a number of flagons of ale the night prior. You know he means "fair one," by Dwyght, but which "fair one does he speak of? The Dwyght who lives near the river crossing, the ford. Ohhh! That Dwyght. Since he lives near the ford and t'other Dwyght is known for being so tall, you and Bruce agree to henceforth refer to the one as Dwyght Ford and the other as Dwyght the Long. (After a number of weeks you both tire of the "the" and Dwyght the Long becomes just Dwyght Long.) As you sally forth along your way to spread the news to the rest of the villagers about the clever new way to distinguish the town's two Dwyghts (and, upon further reflection, perhaps it could also be applied to the three Roberts and those two Audreys), Bruce wipes a bit of sweat from his brow and gets back to shoveling pig feces into a wheelbarrow with his bare hands. It is the middle of the 13th century and what you and Bruce just did was introduce the use of surnames to England. Within another 100 or so years villages all over England will adopt the custom, though it will take longer for all of the future Great Britain to use surnames. Wales will hold out until the middle of the 1500s.
In other parts of the world, the use of surnames - also known as family names, bynames or last names - has already been in use for over a millennia. By the time Rome became a republic around 509 BC the members of its wealthier and classes were already using family names to differentiate themselves or as honorifics (you conquer some land, you get a title, you take it as your surname). In Rome the craze was so strong that most people had three names, the last two of which were both surnames. The man we know as Julius Caesar was actually named Gaius Julius Caesar, with Gaius being his personal name. The For the most part, these names had a common basis for most other family names to follow throughout the world: they were most frequently descriptive of the person's physical characteristic (Caesar meant "hairy") or profession and they were typically passed along from father to child.
This patronymic tradition is still in effect in most cultures today; the father's name becomes the family's surname after marriage. This tradition can be seen in surnames themselves: Anderson means "son of Andrew," Bronson means "son of Brown," Lawson means "son of Lawrence, and so on. (In some cultures, the mother's lineage is still honored through the use of matronymic surnames. In Spanish culture, for example, children are frequently given hyphenated surnames with their father's and their mother's surnames combined.)
The other trait that is typically common to surnames throughout cultures is that they at one time described something about a person quite literally. Bronson meant the in the nether reaches of this family's history there was a progenitor who was known for his dark skin or hair. While patronymic variations of descriptive first names were common, so too was describing where a person lived (Hilton means manor on a hill in Old English), from nicknames (remember Dwyght the Long?) or what a person did (Cooper is derived from the term for someone who makes barrels).
If you're finding that all of this is really floating your boat, you should check into onomastics, a subdiscipline of linguistics, which concerns itself with the study of names. To be specific, the study of personal names is anthroponosmatics, so maybe go learn more about that.