Why some country overvalued or undervalued their currency?

Under-valuation or Overvaluation of currency could be with respect to goods and services

Taking for instance US, over valued US dollars would mean that buying goods and services in the US will be more expensive when compared to what the same dollar amount would fetch for goods and services in China (where currency is undervalued). A tourist would have more bargain for his bucks shopping in China than in the US.

Also, the effect of this is that cost of production in the US would be high and manufacturers would only make little profits from exports/sale of its goods and services. Conversely, in China, the undervaluation of their currency allows for cheap production of goods and expansion of their export market.