If two cells match, return value from third

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I think what you want is something like: 

=INDEX(B:B,MATCH(C2,A:A,0))

I should mention that MATCH checks the position at which the value can be found within A:A (given the 0, or FALSE, parameter, it looks only for an exact match and given its nature, only the first instance found) then INDEX returns the value at that position within B:B.

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