The issue is whether a sentence's meaning is just its truth conditions, or whether it expresses some kind of independent thought or proposition, and this abstract object has truth conditions. These are two quite different approaches to doing semantics.

Why should you care? Personally, I don't see this problem has anything to do with the problem of figuring out how a brain acquires the patterns of connections needed to create the movements and sounds it does given the stimuli it receives. To me it's an interesting but independent problem, and the idea of 'neurally embodied beliefs' is worthless. Some people (with whom I disagree but whom I nevertheless respect) think the problems are related, in which case there's an extra reason to care, and what exactly a neurally embodied belief is, will vary. If you don't care, that's your business.