The answer to this question can be found in the first evening that is described in this book, the night before Santiago embarks on his single voyage to try and catch a fish. Consider the following conversation between Santiago and Manolin:
"Good night then. I will wake you in the morning."
"You're my alarm clock," the boy said.
"Age is my alarm clock," the old man said. "Why do old men wake so early? Is it to have one longer day?"
Clearly, Manolin refers to the way that Santiago wakes without fail very early in the morning. When he calls Santiago, half-jokingly, his alarm clock, Santiago responds by saying that it is age that is his alarm clock, and then reflects on the way that as humans grow older they seem to need less sleep and are able to wake up automatically earlier and earlier. The rhetorical question at the end of this quote is actually quite poignant, as it focuses on the approaching inevitable death of old people and the desire to try and make the most of our lives while we have them.