Weak currency
Usually it is a currency that is going through a trend of being devalued on a regular and persistent basis for a variety of reasons. Often it refers to currencies that are not those of developed countries and thus trade at a discount in relation to those.
Currency traders will regularly take a position on a currency - this means deciding if it will go up or down. With weak currencies that they expect to continue to fall then they can sell it short, and thus make a profit from the fact that exchange rates are volatile rather than static.
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