In the forex market leverage is what makes us turn a 100 pip move into a 100% profit. Leverage is effectivaly borrowing money in one currency to buy another currency.

Most brokers will offer a leverage of between 50:1 to 400:1. This in fact mean that a trader may trade forex to the value of 50 to 400 times their capital.
The amount that is put down is called the margin and needs to be available to hold a position. In a 50:1 the margin will be 2%. In addition to the margin money needs to be available to account for the fluctuations.
A lot is the quantity that forex is sold in. The standard lot is 100 000 and the mini lot is 10 000. Therefore a purchase of 1 standard lot of USD/JPY will cost $100 000 and the purchased of 1 standard lot of EUR/USD will be 100 000 Euros. The lot cost is valued on the base currency.
Bringing leverage into the equation if your broker offers you 100:1 or 1% and you want to buy 1 standard lot of USD/JPY you will need $1000.