One of two; either (of two options). 'Dotchika' (どっちか) is the more colloquial form.
紅茶とコーヒー、どちらか飲みますか？
Tea or coffee — would you like either one?
この二人のうち、どちらかが代表に選ばれる。
One of these two people will be chosen as the representative.
どっちかに電話して予定を確認しておいて。
Call one of them and confirm the plans, please.