Leveraged trading (or gearing as it is sometimes known) is when your fixed sum to invest can be made to be worth more than its value, and in the process securing you bigger profits (or bigger losses).
One common method of explaining leverage (or gearing) is a scenario involving two people, one who is walking, and the other on a bicycle. Although both will be using the same amount of energy (capital) in this scenario, the person on the bicycle is having the results of that energy, the distance (profit), multiplied by the mechanism of the bike.
This is great, except that people are more prone to falling off bicycles, they suffer more in bad weather, and if they're not able to change the size of their gear, when it comes to hilly terrain, they may come to a complete standstill. Added to which, buying a bike in the first place isn't as cheap as just walking.
A somewhat roundabout way of explaining that leverage can be risky. Your profits can be much bigger if you make the right trade, but so can your losses, and if the markets go through a prolonged turbulent period, the small losses that you may have made can become serious losses. There are also financing charges which may apply if you hold positions for protracted periods.
On the other hand, the great advantage of leveraging is that it lets people trade who otherwise wouldn't have the resources. As this example will demonstrate:
Without Leverage
You want to go long on the euro at a position of EUR/USD = 1.500, and you have $1,500 available to invest. You take your position, buy 1000 euros and within a short period the currency strengthens and you sell at EUR/USD = 1.510. Ignoring, for the moment, trading fees and other costs, you've made $10 dollars, not the most inspiring return on your money.
With Leverage
In the same circumstances, you have managed to leverage your investment to be ten times its value. Accordingly, your $1,500 is worth the equivalent of $15,000 and you can buy 10,000 euros. When the value rises to EUR/USD = 1.510, you cash out with $100. Not a bad return on $1,500 of original investment.
Of course, if the Euro had weakened, you'd have lost ten times as much.
This does leave one question, why do companies offer to leverage your money? If we return to the previous example you can work out that the leverage is the equivalent of a short-term loan of $13,500. You sell at EUR/USD = 1.510 for $15,100, and give that $13,500 right back. The lender loses nothing. If, however, you sell at EUR/USD = 1.490, you end up with $14,900, and you're still giving the original $13,500 back, the lender doesn't lose, and if you include some transactional fees and a margin in there, whatever happens, they're going to make a small profit.
There is no inherent harm in leverage on a personal scale, all it does is act like a magnifying glass, profits and bigger, but so are the losses. If you're willing to take the risk, and can deal with the losses, then there's no problem. Until you're very sure of yourself, though, it's best to leverage your trade by the smallest fraction, or not at all, the easiest way to lose a lot of money as a beginner is to take on too much leverage and lose everything straight away.