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The subfigure caption uses []. Because of that, I am unable to use [] in its caption.

\subfigure[ This [] is important]

How do I use the brackets in the caption of the subfigure?

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The problem is that LaTeX views the closing bracket as the end of the short title (optional argument). As suggested by David Carlisle, you can hide the square bracket in a brace pair: {]} should do the trick. (David put the entire optional argument in braces, but this is not needed.) –  Marc van Dongen Sep 14 '12 at 8:53
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For (almost) any latex optional argument you can use {} as in

\subfigure[{This [] is important}]

To hide the inner [] from the argument scanning.

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