Learn Polish: Gdzie on jest?

You don't have to, but it is very common to include it in a short question like this to be clear about who you are looking for. If you just ask Gdzie jest?, it means "Where is he/she/it?" and relies completely on context. Using on specifically means "he".

Why do we use jest here?

Jest is the form of the verb być (to be) that matches the third-person singular pronouns: on (he), ona (she), and ono (it). If you were asking "Where are you?", you would change the verb to match the pronoun: Gdzie ty jesteś?.

Can I change the word order to Gdzie jest on? to match the English "Where is he?"?

Yes, you can! Polish word order is quite flexible. Both Gdzie on jest? and Gdzie jest on? are perfectly correct. Putting the pronoun before the verb is just a very natural way to say it in Polish.

Does on only refer to a male person?

Not always! While on does mean "he" for a male person, it is also used for any grammatically masculine noun. So if you are looking for a masculine object, like a phone (telefon), you would still use this exact sentence to ask where it is.