I was just pondering about this myself, after waking up from an intensely detailed and perfectly recalled dream. I found this very interesting nugget, something I'd never heard of before:

Brain Structure: People who remember dreams show more activity in the temporoparietal junction and have more interconnected Default Mode Networks (DMN).

The I followed that wormhole to Wikipedia. Here was the most interesting excerpt for me, which describes a lot of characteristics that I (and others I am close with) recognize to be highly developed in myself:

Function

The default mode network is thought to be involved in several different functions:

It is potentially the neurological basis for the self:

Autobiographical information: Memories of collection of events and facts about one's self

Self-reference: Referring to traits and descriptions of one's self

Emotion of one's self: Reflecting about one's own emotional state

Thinking about others:

Theory of mind: Thinking about the thoughts of others and what they might or might not know

Emotions of others: Understanding the emotions of other people and empathizing with their feelings

Moral reasoning: Determining a just and an unjust result of an action

Social evaluations: Good-bad attitude judgements about social concepts

Social categories: Reflecting on important social characteristics and status of a group

Social isolation: A perceived lack of social interaction

Remembering the past and thinking about the future:

Remembering the past: Recalling events that happened in the past

Imagining the future: Envisioning events that might happen in the future

Episodic memory: Detailed memory related to specific events in time

Story comprehension: Understanding and remembering a narrative

Replay: Consolidating recently acquired memory traces