We understand sentences by means of "verbal working memory" a temporary store for the words of a sentence. I discuss VWM briefly in my book Eve Spoke: Human Language and Human Evolution, published by Harvard University Press. The chapter "Human language and the reptilian brain: The sub cortical bases of speech, syntax and thought" discusses this topic in detail. You can also read about verbal working memory in books authored by Alan Baddeley, for example Working Memory (Oxford Psychology Series No. 11.