'dress up for success' is a misquotation IMO -- the usual phrase is 'dress for success', which means 'wear clothing that shows that you are successful, and you will be successful'.
In part this a sort of mental trick of salesmen and managers, who believe that your chances of success are better if you 'look the part' (and in certain situations they are doubtless right; or at least success is more difficult if you don't look the part), and in part it's a sort of psychological trick -- if you think you're well prepared to meet challenges, including being properly dressed, your will have more confidence and thus have a better chance of success.

Of course, it's also a motto highly favoured by clothing merchants ;-).

By contrast, 'dress up' means to wear especially, fancy, formal, or otherwise special clothing (e.g. 'we all got dressed up for the party')

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Note added at 20 mins (2008-07-04 14:56:33 GMT)
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sorry -- that should read '...to wear especially fancy, formal,...'.

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Note added at 2 hrs (2008-07-04 16:43:02 GMT)
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FWIW, a bit of googling suggest that some native English speakers do use 'dress up for success' in the sense of 'dress for success' (at the rate of around 3,500 and 600,000 ghits, respectively). sometimes knowingly (and thus humorously) but usually unknowingly.

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Note added at 20 hrs (2008-07-05 10:53:29 GMT)
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Given the additional context and the typical age group of chatsite users, I'd say that the sexual innuendo is unmistakeable here. In this context,among other things 'Dress (up) for success' means 'if you want to make it with your date, you have to dress accordingly' (applies to both sexes).