That way; that direction or place located away from both the speaker and listener (polite).
出口はあちらの方です。
The exit is that way.
あちらをまっすぐ行くと駅に着きますよ。
If you go straight that way you'll reach the station.
あちらをご覧ください。
Please look over there.
That (one); a thing that is distant from both speaker and listener or is not visible but known to both.
あちらのコートを試着してもいいですか。
May I try on that coat over there?
あちらの席は空いていますか？
Is that seat over there free?
説明書はあちらの箱の中にあります。
The instruction manual is in that box over there.
That person; a polite way to refer to someone distant from both speaker and listener or not present but known to both.
あちらが部長の田中さんです。
That over there is Tanaka, the department manager.
あちらは来週から出張する予定です。
He/She is scheduled to go on a business trip from next week.
あちらの方とは以前に一度お会いしました。
I met that person once before.
There; over there; can also refer to a foreign country (especially Western countries) depending on context.
あちらはもう雪が降っているそうです。
I hear it's already snowing over there.
あちらの国では休日の習慣が違います。
In that country, holiday customs are different.