Introduction to Calculus and Analysis, by Richard Courant and Fritz John. This book clearly explained many of the motivating examples of the concepts in Calculus, which was important to me as a beginning student. Too many times I read math textbooks that simply present a list of definitions, theorems, corollaries, and whatnot, failing to guide readers from one point to another. I agree that for advanced level of math, there're probably no good motivations or 'storyline' that weave these constructs together (they're purely symbolic); however, for a layman level, I feel it's crucial to at least make the readers understand why and how these concepts come to be, so that they can grasp at least a little bit of the 'logic' of math.
Similarly, Analysis I by Terence Tao has a 'Why do analysis' that has made me actually enjoy analysis.
This book broke down a hard and mysterious topic (operating systems) for a new CS student like me into everyday analogies, which almost eradicated my fear of the subject matter. It had the appropriate amount of technical details to be usefully informative for a college class while also inspiring a more in-depth read of other material that are much more boring. The book is the reason why I love operating system so much, and I continued to take more CS classes as a math major.
Similarly, Analysis I by Terence Tao has a 'Why do analysis' that has made me actually enjoy analysis.