Learn Turkish: Onun kocası polis. - Her husband is a police officer.

Because we are talking about someone's husband! In Turkish, when we say his, her, or its, we add a possessive suffix to the noun. The root word for husband is koca. Because it ends in a vowel, we must use the buffer letter s before adding the 3rd-person suffix -ı, making it kocası.

Does onun specifically mean her?

No, Turkish pronouns do not have grammatical gender. Onun means his, her, or its. We translate it as her husband here based on common sense context, but grammatically it could easily mean his husband if we were talking about a married man.

Can I drop the word Onun and just say Kocası polis?

Yes, absolutely! Because the -sı suffix on kocası already tells us that the husband belongs to a third person (his or her), the word onun is optional. You only need to include it if you want to emphasize that it is HER husband and not someone else's.

Where are the words for is and a in this sentence?

Turkish often leaves out the to be verb (like is) for simple present tense statements in the third person. Also, when stating someone's profession, Turkish usually drops the word for a (bir). So, saying Her husband police is the perfectly natural way to express Her husband is a police officer in Turkish.