That's a nice Hebrew thing (ok, IMO at least) - you take a name of a place, like הבית, ירושלים, מצרים and so on. You just ad a ה in the end, which makes a "A" sound and that implies direction towards that place.
The latter example, מצרים, appears fairly often in the bible - מצרימה, means that someone or something went to Egypt.
So הבית means "the house, the home" and הביתה means "towards the home" or "in the home's direction". Standing alone that sounds like an imperative, telling someone to go home, so the closest English translation would be "go home".
Hope that helps :)
It's not unusual for a parent to say to a child, sometimes if they're behaving badly, "Home, now!"; "To your room, [now]!"; or "[Alright] to bed [everyone]."—often prefaced by the name(s) of the child(ren) and accompanied by pointing toward the target-destination. Short, even single word expressions are not uncommon in communication when context together with other linguistic and paralinguistic features cover the rest (e.g., intonation, tone, stress, gesturing, facial expressions, the surrounding environment, and the overall communicative situation). So we actually do the same thing with constructions such as "[destination]", "to [destination]", and probably many others.
So I guess it means homeward, which we can't use by itself in English (although we can just say "onward").
I assume you can't do that with any place, like בית ספר? What are the limitations?
You can say it with בית ספר, that will be בית הספרה, but that's unusual. I think the limitations are that the noun used should be a place, and in case of סמיכות, as in בית ספר you should use the סמיכות rules to make the noun definite.