What is the difference between "my" and "my own" and also what is the difference between "its" and "its" and "its own"?
This is my book.
This is my own book.
This is its cover.
This is its own cover.
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The variant with "own" has a stronger sense of possession or ownership, and is often used to indicate that the possession is exclusive and not shared with anyone or anything else.
Let's meet at my house.
Here, "my house" is just the place where I live. I might or might not share that house with roommates or family; it's not really specified one way or another.
I am saving money to buy my own house.
Here, I'm saying that my intent is to buy a house that belongs to me and only me. Maybe I live with roommates now, and I want to be more self-sufficient.
I find it difficult to imagine a situation where I would refer to a book's "own cover," but one common phrase where "its own" is used is "on its own merits." For example:
You should judge the plan on its own merits, not on the person who proposed it.
Again, this is using "its own" to be exclusive. It's saying you should only consider the good and bad points of the plan when judging it; you should not consider the good and bad points of the person who proposed the plan.
This answer could take pages, so let me just add to Canadian Yankee's answer.
In some contexts own could be paraphrased as "original".
Is that your own hair, or a wig?
Is that the book's own cover, or was it added by the library?
Sometimes own is an intensifier of the closeness of the relationship and could be paraphrased as "even his own":
He's so crooked he'd cheat his own mother.
here, "even their own":
Some animals have such a strong instinct to free themselves from a trap that they will chew off their own foot to get loose.
Sometimes it means "by myself, with no interference or annoying suggestions from you":
If you don't mind, I'd like to choose my own necktie, thank you.
Sometimes it means "not yours" or "not the one you have":
You go on without me and I will meet you there. I'm going to take my own car.