This is a different kind of class and math book. You may be used to mathematics where you compute something, whether you solved an equation, differentiated a function, simplified an expression, determined a limit, or evaluated an integral. You may have worked on applying theorems (such as the Squeeze Theorem for limits) and have built strategies for a certain problem type (sorting out when to integrate using substitution versus when to integrate by parts).
The majority of your mathematical experience so far may have been computational in nature. However, when you rely on theorems from calculus, how do you know that what you rely upon is solid? If this text is in front of you, it is because you are now at a place in your mathematical career where computation can be put aside for a moment so that you can learn how to read and write mathematical proofs.