Broadly, Western philosophies have typically defined one's "self" (or assumed "self" to be) the guiding force behind one's brain and body.
Eastern philosophies, in contrast, have tended to consider the self a sort of emergent property of other processes: something akin to an illusion that we find to be reassuring or useful, as opposed to a real-deal thing that's actually in charge.
For many in the West, because of this traditional definition, it can be disturbing to think that we—the "I" that we perceive ourselves to be—are not the ones in the driver's seat, but rather a convenient, calming sort of filter over a more complex, difficult-to-parse reality.
In Buddhism, anattā means something like "non-self," and recognizing and achieving a calm and peaceful acceptance of this reality is a goal considered to be worthy of pursuit.
In many Western practices and ideologies, though, that pursuit would be seen as something akin to irresponsibility or even blasphemy: I am me, I live in this world and control my thoughts and actions, and the idea that I do not would mess with my self-definition as an individual who is in control of my own destiny.
Many aspects of modern neuroscience—and most of it is modern, as the tools that were invented and deployed over the past few decades have taught us essentially everything we know about how the brain works (everything before that was massively incomplete or incorrect)—seem to align more closely with the Eastern perspective, as although we do have an aggregated sense of "self" that feels very real and organism-defining and monolithic, that self seems to be a narrative that the left-hemisphere of our brain creates to help us interpret what's happening across a more dispersed self.
Said another way: we take in information about reality—external and internal—and one of the ways our cognitive apparatus helps us interpret and understand all that data is by turning it into a storyline that we tend to parse via a first-person perspective.
That perspective is real, as we are entities and our brains are soaking-up and filtering all that data for use.
But our sense of self within that deluge (and the processing system handling it) seems to be an illusory shape create by all those processes, rather than a thing that exists as its own, single, separate creation.
As far as we can tell, there’s no part of the brain where the “self” or “consciousness” resides: that sense seems to be emergent from all these other activities.
The self is more of a verb than a noun, then, because the self is the amalgamation of all those processes, including those that cause us to ruminate about the past, make predictions about the future, and worry about threats and opportunities in (what we perceive to be) the present.
There's a lot to be gleaned from this collection of findings and framings, including explanations for why psychedelics and other drugs will sometimes seem to blend our consciousnesses into a sort of universal consciousness, and possibly why we have so much trouble ridding ourselves of persistent issues related to self-criticism and doubt (the interpretive parts of our brains that create our "self" narrative can't really be turned off: only managed and responded to healthily).
None of which matters for our general, day to day existence; the fact that our sense of self might be the consequence of our brain telling us stories about sensory information we encounter rather than a chunk of brain matter that is a separate thing does not in any way change our experience of feeling like an entity that is at the wheel, in control, and able to steer our brains and bodies wherever we want to go.
It can be useful to have this framing available, though, in part because it's where science seems to be going, and knowing about it can help us understand impending discoveries and similar revelations, but also because it might help us better deal with intrusive thoughts, persistent psychological issues, and other elements of conscious life that otherwise might not seem to make much sense, and which we might struggle to cope with if we assume we're in control and are thus failures for not better handling these negative psychological issues.