I think Ravi's answer was very precise and really doesn't need any further explaination, unless you are expecting a step by step guide on what to do. I think you could find further examples of how people used those, by performing a search here, or looking at your existing system(unless it is brand new).
Honestly a BADI either helps to meet your business requirement or it doesn't. My ideal use of a BADI may never match your use either 
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Take care,
Stephen