What is the meaning of the eigenvector and eigenvalue ? Why is that so interesting/important?

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I asked many people those questions and everybody can calculate the eigenvector and eigenvalue of a given example, but if I ask those people what does it mean I always see frozen faces and and get an ehhhh. So, I'd be happy if someone can give me response for those questions and doesn't ask me if I've already asked Google or Wikipedia. By the way, I've seen that this question was asked in a similar way, but isn't there a short explanation for that ?