A private room is a room that is not shared with other people from the hostel- in other words, you book and pay for all the beds in the room.  If you are travelling alone, for example, but want to book a double room, you must pay for two people in order to book the whole room.  (That's why the option to book for one person in a double room, for example, isn't available in the select box.)

• Single - Is a private room with one (single) bed for one person
• Double - Is a private room with one (large) bed for two people
• Twin - Is a private room with two single beds for two people