I cannot understand words of [of its own] after noun. I checked some meanings but I cannot get the core meaning.
Such as a significance of its own and some costs of its own are used as different meanings. first one is used like “specific” second one is used like “one’s self”.

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Yes - it is difficult I think.

part of the CORE meaning ( you used these words well!)
has to do
with the THING or Object ( it, book, shopping cart)
OR
the person

both - having an individual life, or kind of like a SELF
behaving like they are Person - who can make decisions
or a special book that is on this ONE topic.

a life of its own,
a mind of its own,
a book of its own

They ALL have something that is like a SEPARATE EXISTENCE

The thing is - the metaphor is only taking this thread of meaning
and USING it to express THE SEPARATEness -
the state of being distinct
and separate.


Do you know when a 2 year child begins to toddle away ( walk away a little ) from his mom?
He is learning about becoming his OWN separate SELF.
He is learning a little about being separate from Mom.

This metaphor is talking about that THREAD of meaning.
Being a toddler, being separate.

But the metaphor GOES NO further than that! It is using just that little thread of meaning.
It is talking about being a toddler- THAT LEVEL of being separate.
So not so developed - very young - age 2!

Does that make sense to you?
It’s very subtle actually.