どちら means "which (of 2) ways or directions" By implication, it can also mean which of 2 people or things (it's more polite to identify someone by their relative direction, rather than to them directly). Examples are like "Which way should I go?, "Which one is he?" "Which item should I choose?", etc. どっち is the casual form, among friends or if thinking out loud. どれ is a choice of 3 or more or any potential directions, people or things.
they really all mean the same thing; it's just the politeness level that's different. どっち is the most casual, and どちら is the most polite. But they all are "which (one)?" asking for a choice between at least two objects (or people, etc)
