According to Wikipedia, the Currency Act refers to a pair of acts passed by Parliament that regulated the flow of paper money in the colonies in North America. Because there were no gold or silver mines in the colonies, the colonists constantly had a shortage of money that could only be obtained by trading with Britain. To combat the effects of this, the British Parliament enacted the Currency Act.
The British colonies in America were not tremendously resource-rich places when they were first settled. As such, the only way they could obtain currency was through trade, and what little currency they had could not be backed by any physical capital. Some currency was backed by loans, other by land. There was no standard, so the currency depreciated. As UShistory.org explains, British merchants were understandably concerned, because the American currencies were very volatile. In response, the British Parliament passed two pieces of legislation to regulate currency: the Currency Act of 1751, and the Currency Act of 1764.
The first Currency Act, in 1751, restricted the issuing of paper money from New England. Unfortunately, more paper money was issued than was taxed by the British, so inflation resulted, as Wikipedia explains.
The second Act, in 1764, prohibited the issuing of new currency and the reissuing of old currency to control inflation rates. This solved the regulation of currency by simply abolishing the paper money in the colonies. Colonists, including Benjamin Franklin, protested in England. The Currency Act resulted in continually rising tensions between the colonies and the British government.