This is a niche example of public-facing linguistics. In his earlier books (especially The Language Instinct, Pinker tried to give an overview of linguistics (from phonetics to syntax to semantics and sociolinguistics), covering various different aspects of language to show how even the most curious trivia can be explained through the discipline of linguistics. To put it simply, this book is primarily concerned with irregular verbs. Why is it that the past tense of "string" is "strung" (and similarly "sting", "stung") but the past tense of "bring" is "brought" and the past tense of "ring" is "rang"? How do speakers know when to add -ed to a verb and when to use an irregular alternative, and how do they know how to form the irregular word? Sometimes the irregular form involves a vowel change (dig-dug, fight-fought, hang-hung), sometimes it involves a devoiced ending (send-sent, lend-lent), sometimes a vowel change and devoicing (keep-kept, sweep-swept) and sometimes no change occurs at all (hit-hit, cut-cut). The same is also true of nouns where English has a default -s marker (bed-beds, car-cars) but also several irregular umlaut nouns (man-men, foot-feet, mouse-mice). While these irregular forms can be explained diachronically by historic vowel shifts, there is no hard-and-fast rule for English speakers today ("shrink" becomes "shrunk" but "think" becomes "thought"). Children must memorize these irregular forms independently.
Pinker is often lumped together with Chomsky as one of the leading advocates of universal grammar but this is not an accurate characterization. Pinker believes that the human brain has an instinct for language, a multi-process computational apparatus spread across different regions of the brain. It is not a preset rulebook of grammatical parameters like Chomsky's x-bar theory. In this book, tackling the specifics of irregular verbs, Pinker shows instead that two cognitive processes are involved in language: the brain clearly memorizes a word and information about it (a root morpheme, its meaning, its grammatical classification, and any irregular form) and then also learns a series of phonological, morphological and syntactic rules (add -ed to verbs to form the past tense, devoice the "d" if preceded by an unvoiced consonant; add -s to make the plural, voice the "s" if the preceding sound is a voiced consonant). The brain retrieves the word but only applies morphological rules if the word calls for it. Chomsky wanted to show that all language production is the result of some pre-programmed principles (e.g. speakers don't just learn that "thought" is the past tense of "think"; the brain has some mysterious root for both words and derives "think" for the present tense and "thought" for the past tense"—a hidden morpheme beneath the surface of daily speech). But looking at both traditional linguistics, as well as psycholinguistics and neuroscience, Pinker shows how the brain produces language through a variety of cognitive procedures working in tandem.
I thought there was a lot of interesting tidbits throughout the book. For example, Pinker develops a lot of argument out of the fact that, in compound nouns, only irregular nouns permit the plural (e.g. we can say "mouse-infested" and "mice-infested"; however, while we can say "rat-infested", it is awkward to say "rats-infested"). This suggested that irregular plural "mice" is not seen as some inflectional derivation of "mouse" but as an alternative root morpheme. Pinker's theory also cogently shows why we produce regular endings for compound words: for many, the plural of "lowlife" is "lowlifes" rather than "lowlives"; the plural of "still life" is "still lifes" and not "still lives"; the plural of "Mickey Mouse" is "Mickey Mouses" and not "Micky Mice". In each of these cases of bahuvrihi nouns, the compound is not technically headed by an irregular noun (a still life is not a kind of life, Mickey Mouse is not really a kind of mouse but a cartoon name), and so the default morphological rules now apply. We can see in our language use how both lexical data and morphological rules work concurrently.
Although written for a general audience, it is a little specialist in topic, but it's a good example of linguistics scholarship which shows how we have an innate understanding of grammar in our brain, rather than Chomsky's hypothetical machine.