Brandom has a gift for distilling complex ideas into a digestible form for the learned and the unitiated alike, so much so that reading his prose the reader is transported into one of his lectures.
As a philosopher, he moves and breathes in the tradition of inferentialism, which is a distinct kind of rationalism as well as being a conceptual realism; the world is conceptually/inferentially articulated without being causually dependent on the mind. Not only is this the case but that objects in the objective side entail and exclude other objects in the same way that in on the subjective side our takings-of-the-world-to-such-and-such (i.e. commitments) embrace and repel other takings.
But whereas it is either necessary, possible or impossible for an object to entail other objects and exclude other objects, it is merely "impermissible" (48) for a single subject to hold mutually incompatible or contradictory commitments; the subject has a duty (deontic) to ensure maximum consilience between the beliefs they hold. So according to Brandom, stubbornly insisting on integrating such materially incompatible commitments threatens the integrity of the transcendental unity of apperception--an ongoing process of rational synthesis by virtue of which we earn our sapience.
The beasts of the field, including our mammalian, avian and cephalopodic cousins are sentient. But we humans are sapient in addition to being sentient. Sapience isn't a quantative leap from sentience. Likewise, an impressive mastery of of an array of reliable dispositions to differential reponses ("red", "red dress", "red blouse") nonetheless does not amount to concept use, of which descriptions proper form the lowest level of hierarchy. To be a description a word has to stand in relation of inferential inclusion and exclusion to other labels and must be available as a premise to or a conclusion of an inference. As concept users and concept-mongerers, we aren't just denizens of the natural world, we are also citizens of the social world. Our vocabulary to make things explicit, and so to contribute to the labor of the concept, ranks among the crowning achievements of our species.
Now a few words of criticism. Brandom innovates on Kant's teaching on the transcendental synthesis along the pragmatic dimension; sapience is accordingly framed as a kind of semantic self consciousness. Sapient creatures like us, sensitive as we are to the "normative force of better reason" (128), have the lifelong duty to unpack our commitments, endorsing appropriate consequences and rejecting those beliefs that stand a relation of materially incompatibility with the former commitments in a "game of giving and asking for reasons" (119), without which no other language games are possible. Granted this point, it is still a bit suspect to expand Kant's transcendental synthesis along the lines of semantic self-consciousness. After all, did not Kant abundantly made himself clear that the various transcendental syntheses, including and especially the transcendentally synthesis of apperception, happens behinds the back of our heads, so to speak? From the perspective of this restricted definition, Brandom's innovation appears not so much an ampliative reading of the transcendental synthesis as it is a description of a process grounded in the latter. Brandom goes on to consolidate the Kantian point that the institution of norms (binding oneself by rules of one's own making) make positive freedom possible. Still, I would venture to claim that this semantic freedom of concept users is not to be identified with the transcendental synthesis itself.
Furthermore, I am not completely comfortable with Brandom's deflation of truth and the notion that truth does not accomplish the explanatory work that we naively assume it does. Perhaps contemporary proponents of scientific realism would disagree with Brandom on this acccount.
That being said, it is to Brandom's credit that he is able to weave together the key rationalist insights on how we acquire concepts and what concept use entails in the work of Kant, Hegel and all the way to Frege and Sellars, and present them in a clear and succinct narrative, making explicit what was all along implicit in the rationalist tradition. I would recommend this book to anybody who is looking for a decent hands on introduction to what kind of job philosophers do.