What it is:
A weak dollar is used to describe the United States' currency decreasing in value relative to other currencies.
How it works/Example:
The dollar's value is fluctuating all the time. Sometimes you can buy more with a certain number of dollars, and sometimes you can buy less.
For example, if you needed $100 to buy a gold coin yesterday, but today you need $110, the weakening dollar is causing you to pay more for the same amount of gold.
Currency value is relative. The dollar can be weak relative to one foreign currency, but strong relative to another country's currency.
It helps to remember that currency is a commodity, like orange juice or pork bellies. When you exchange dollars for Yen, for example, you're "selling" your dollars and "buying" Yen the same way you would be if you were "selling" your dollars and "buying" orange juice.
Currency, like every asset, is ruled by supply and demand. When demand for dollars goes up, the price goes up, and vice versa. So in our example, if everybody is trying to "buy" Yen (that is, convert their dollars into Yen), the price of Yen is going to go up and Yen will be described as a strong currency. Since the price for Yen is going up, you need more dollars to "buy" the same amount of Yen. Yen is the strong currency, and the dollar is the weak currency.
Why it matters:
For everyday items -- think clothes, electronics and auto parts -- people will almost always buy whatever is least expensive. So, when the dollar weakens (that is, when American-made stuff gets relatively cheaper), American exports tend to increase. The opposite is also true -- when the value of the dollar rises, American-made products are more expensive overseas.
Most people tend to think a strong dollar is preferable to a weak dollar, but in reality, it depends on where you stand. An American factory worker would probably prefer a weak dollar because then the factory could increase exports to the rest of the world, and the worker's job would be much more certain. A person who wants to buy a Mercedes would probably prefer a strong dollar, since dollars would be worth more relative to Euros, making the foreign car relatively cheaper.
Currencies are always fluctuating relative to each other, and some investors trade currencies like others trade stocks. If you can figure out what will make the price of a particular currency weaken, you're in a position to make a lot of money.