Examples

Here, his indicates that the finger belongs to the thief. Gross.

Think about how this sentence would look without the pronoun: The would-be thief left the would-be thief's severed finger at the crime scene. Now that's a horror scene.

Note: It's a hotly contested subject whether "his" in sentences like these are adjectives or pronouns. Some people say that since "his" comes before a noun and somewhat modifies "severed finger," it's an adjective. Others say that it's a noun marked with the genitive case, which is just a fancy way of saying possessiveness.

Well, as fun as grammar debates may be, we're not going to go there. So we're just going to call it a pronoun (but maybe an adjective).

In this case, mine shows that the ownership of the cake has been claimed by Becky. Everyone else is out of luck.

Your shows that the poodle belongs to Chris. My indicates that the missing car keys belong to the speaker who's really wishing that the Geico Gecko offered poodle insurance right about now.