Bitcoin is a currency like no other. In short it's digital money that solves many of the problems our current currencies suffer from and introduces many other uncertainties we never had to deal with before.

Benefits

Low inflation risk. One of the biggest problems with our current dollars and other currencies used around the world is inflation. Over time all currencies lose purchasing power at a rate of few percents per year mainly because governments keep printing more money. This process is basically a small tax on your accumulated wealth. With Bitcoin you don't have this problem because the system is designed to make Bitcoins to be finite. Only about 21 milion Bitcoins will ever be released (mined). The release of new Bitcoins is slowing down and it will stop completely within a few decades. We have a slowing population growth which is projected to stop at around 10 billion by approximately 2050 which roughly coincides with the last Bitcoin to be mined. There will be roughly 1 Bitcoins for every 500 people.
Low collapse risk. Regular currencies depend on governments which fail ocassionally. Such events either cause hyperinflation or a complete collapse of a currency, which can wipe out savings of a lifetime in day. Bitcoin is not regulated by any one government. It's a virtual global currency.
Safe, simple and cheap. The problem with traditional online transactions from the perspective of the seller is that Credit cards, PayPal you and other online payment systems allow buyers to claim their money back. You can can use escrow services but that makes things complicated and slow. With Bitcoins once you have the money you have it and that's that. Buyers can not in any way take the money back and the seller can safely ship the product or perform the service that the client purchased. From the buyer's perspective the infrustructure for payments and sending money between accounts is potentially going to be simpler and cheaper because it is peer-to-peer rather than done through some intermediary.
Easy to carry. Not a real problem that needs a solution, but you can carry a billion dollars worths of Bitcoins on a memory stick in your pocket. You can't do that with cash or even gold.
Untraceable. This is both a benefit and a risk for Bitcoin. The benefit is that you don't have to be afraid of any organization of being able to trace the source of your funds. This is a clear benefit in many areas of the world because governements that are supposed to guard against fraud are actually defrauding people by taking their savings partially or fully. Regarding risks I will discuss them in the next section.
Risks

Untraceable. This feature of Bitcoin of also attracts crime. People can buy and sell drugs and other illegal items with significantly less risk of being traced by authorities. Bitcoins in this regard are similar to regular cash which is used by criminals. This fact may bring unwanted attention from governments that will outlaw Bitcoin.
Easy to lose. If your credit card is stolen or somebody hacks into your bank account there is a good chance you will not lose any money as banks will fix your balance. Even cash can be potentially recovered if the police acts fast. But with Bitcoin if you lose it you lost it for good. There is no mechanism to recover stolen or lost Bitcoins. If somebody hacks into your wallet where you store your Bitcoins you lost them for good. The best way to store your Bitcoins is on disk that is disconnected from the internet.