He is = On jest. I can't understand why do they translate it as a single word "jest"!? I would understand it if there was a question " Is Jola/Marek at home" the short answer would be" Jest".
Well, technically we can omit the pronoun even in 3rd person. And actually your example is good (if we take Marek): For an English question "Is Marek at home" the answer is "He is", and in Polish the answer can easily be "Jest".
Polish verbs don't usually need the personal pronoun to be stated, so it can mean is, he is, she is, it is and even you are (but only when used with the the pronouns pan/pani). So jest (and other verbs in the 3rd person) often do include the pronoun to clear up any ambiguity, but it's not incorrect to omit them (when referring to he/she/it, the formal you always includes the pronoun).
Oh, no, pan/pani jest means you are. My bad. But it's specific, you know. I mean, normal usage of jest can't be used as you are elsewhere than in the formal, polite talk. And if you say about something else, you can omit on/ona/ono etc., so you have jest. However, when you want to say (pan/i) jest, you can not omit pan/i.
Oh okay, I see what you're saying. Edited my original post to (hopefully) make it a little less confusing.
It's probably safer to say, that in formal speech we use third person with gender and number appropriate pronoun (pan/pani/panie/panowie/państwo and a few more that are less common). And it's not just for this one verb, but in general.
Gramatically, „jest on” and „on jest” have the same meaning. You wouldn't see „jest on” in a single, independent sentence, but in some longer writing you may encounter such inversion to make the text flow better.