I've often written about developer velocity, but haven't formally defined it. In general, velocity is speed with direction. So I think of it like this:

Developer velocity is a measure of productivity related the rate of software changes.

Developer velocity isn't the whole of developer productivity. I think of developer velocity as post-commit workflow. Once a feature or change set is ready, how much "red tape" is there to get those changes out to customers? But "red tape" isn't just bureaucratic with software.