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The article of Richard Hain "Lectures on moduli spaces of elliptic curves", arXiv:0812.1803, is a very good introduction to the subject, wich which contains a lot of motivations. Here you can learn many things about orbifolds, and there is also an appendix on stacks.

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The article of Richard Hain "Lectures on moduli spaces of elliptic curves", arXiv:0812.1803, is a very good introduction to the subject, wich contains a lot of motivations. Here you can learn many things about orbifolds, and there is also an appendix on stacks.