The Batman centered on a Bruce Wayne that wasn't as experienced as we've seen him in many previous Batman adaptations. He was younger and still learning the ropes of the superhero/vigilante business. As was to be expected, being a night-based crimefighter who was just starting out came with its difficulties — mainly the lack of sleep, as Bruce stated near the beginning of the film: "These nights all roll together in a rush, behind the mask."
As such, Wayne had a few strategies to keep things straight and remember everything he would go through as the Caped Crusader. One of them was a journal in which he kept track of his daily activities. It was a humanizing idiosyncrasy for the Dark Knight, and director Matt Reeves has revealed the cool pop-culture and real-life inspirations behind it.
On the Apple-exclusive director's commentary, Reeves discussed Bruce's journal, stating that it was inspired partly by Taxi Driver protagonist Travis Bickle (played by Robert De Niro) and Robert Louis Stevenson's 1886 novella "Strange Case of Dr. Jekyll and Mr. Hyde" (at the 6:37 mark):
"[I] wanted him to have this almost Travis Bickle-like quality of keeping a journal. And it was really inspired — a little bit — by Dr. Jekyll and Mr. Hyde; the idea of Dr. Jekyll charting [his] experiment — seeing what the effect of becoming Mr. Hyde is on him and what happens to him, and then keeping track of it and writing it down."
The director then revealed that Bruce's journal-habit was partially inspired by a rookie police officer: "[I] thought, 'Okay, we have a year-two Batman. This isn't an origin tale. We're gonna start right inside of his head, and how do we do that? Let's start in his journal, and the journal will be a recording of the nights, when he goes out into the city.' And I actually — when I was writing — also found a journal online from a rookie cop. The first year of his career. [He worked the night shift], and he talked about becoming a nocturnal animal, because he was coming out at night. And I just thought that was so great, and I thought it so spoke to this idea of Bruce going [out]."
The Batman portrayed its titular character in a more realistic and somewhat unsettling light than prior films (excluding several elements from Christopher Nolan's trilogy), so it makes sense that something as seemingly ordinary as a police officer's journal and as dark as Taxi Driver inspired Bruce Wayne's proclivity to write down his nightly activities.
It may seem like a small detail, but the journal played a pivotal role in the film and its atmosphere. Not only due to how prominent Bruce's narration was, but also because it served as a useful storytelling tool, given how it clued audiences in on Bruce's troubled mental state from the beginning.
The Batman is currently available on HBO Max and to own on digital.