Carl Zimmer has put together this week's news about language evolution. In one paper, mice with knockout versions of the FoxP2 gene were found to have trouble with their squeaks! In other words, the gene may be involved in vocal communication in most mammals. The second paper demonstrates the existence of a neural area homologous with Broca's area in macaques. This would show that one cortical region underlying language function in humans is broadly shared among anthropoid primates, although not elaborated to the extent found in living and fossil Homo.
Both of these are stories about homology. Humans aren't unique in the presence of either FoxP2 or Broca's area. Instead, these emerged long ago. Both of them may have been involved in vocal communication for a long time in our lineage, in other primates, and potentially in many other mammals.
So human evolution didn't have to originate new language-related functions for these elements out of whole cloth. There was already a simple structure there to work with. Human evolution elaborated on this ancient foundation.
The details, of course, remain to be worked out. FoxP2 is far from the only gene related to language, and Broca's area is far from the only cortical region. Different areas may have yet other origins, may have been put together in new ways during human evolution, and may have been expanded upon (or in some cases possibly even reduced) to result in our unique configuration.
Anyway, read Zimmer, and I may write more on the Broca's discovery later.