Interestingly, the spread of surnames almost always coincides with the development of states: surnames were originally an instrument by which the state could categorize its citizens for purposes of taxation, conscription and control. Hence, we first see them in Imperial China and only in Europe much later; and their spread can be traced to the reach of the state into a particular area. So, in Britain, the southerners got them first, then the north, and finally Wales and Scotland.
There isn't much need for a surname when you're sat in a rural community and a name like "Peter son of Michael" or "Peter who lives near the river" will do; but this sort of description is obviously useless to an outsider, like a taxman, who never knew Michael and doesn't know where the river is. So the state would initially assign people surnames which would be used only in their records. But then, as the impact of things like courts, tax rolls and land registers became more ubiquitous, their use would become increasingly common - after all, I want to make sure the legal system knows I've paid my taxes and that my land belongs to me. Capitalism and modern transportation technology had a lot to do with this as well - as people increasingly moved and traded across boundaries, it was important to be able to differentiate between different Peters and have a gold standard of recognition which made him nearly unique.
The exception, of course, was the aristocracy, whose names usually derived initially from where they lived, and denoted their status as owners of that territory. But for those of us who aren't of noble blood, I'm afraid we initially got our surnames so the taxman could find us more easily.