1 - Decentralization
Bitcoin's most important characteristic is that it is decentralized. No single institution controls the bitcoin network. It is maintained by a group of volunteer coders, and run by an open network of dedicated computers spread around the world. This attracts individuals and groups that are uncomfortable with the control that banks or government institutions have over their money.
Bitcoin solves the "double spending problem" of electronic currencies (in which digital assets can easily be copied and re-used) through an ingenious combination of cryptography and economic incentives. In electronic fiat currencies, this function is fulfilled by banks, which gives them control over the traditional system. With bitcoin, the integrity of the transactions is maintained by a distributed and open network, owned by no-one.
2 - Limited supply
Fiat currencies (dollars, euros, yen, etc.) have an unlimited supply - central banks can issue as many as they want, and can attempt to manipulate a currency's value relative to others. Holders of the currency (and especially citizens with little alternative) bear the cost.
With bitcoin, on the other hand, the supply is tightly controlled by the underlying algorithm. A small number of new bitcoins trickle out every hour, and will continue to do so at a diminishing rate until a maximum of 21 million has been reached. This makes bitcoin more attractive as an asset - in theory, if demand grows and the supply remains the same, the value will increase.
3 - Pseudonymity
While senders of traditional electronic payments are usually identified (for verification purposes, and to comply with anti-money laundering and other legislation), users of bitcoin in theory operate in semi-anonymity. Since there is no central "validator," users do not need to identify themselves when sending bitcoin to another user. When a transaction request is submitted, the protocol checks all previous transactions to confirm that the sender has the necessary bitcoin as well as the authority to send them. The system does not need to know his or her identity.
In practice, each user is identified by the address of his or her wallet. Transactions can, with some effort, be tracked this way. Also, law enforcement has developed methods to identify users if necessary.
Furthermore, most exchanges are required by law to perform identity checks on their customers before they are allowed to buy or sell bitcoin, facilitating another way that bitcoin usage can be tracked. Since the network is transparent, the progress of a particular transaction is visible to all.
This makes bitcoin not an ideal currency for criminals, terrorists or money-launderers.
4 - Immutability
Bitcoin transactions cannot be reversed, unlike electronic fiat transactions.
This is because there is no central "adjudicator" that can say "ok, return the money." If a transaction is recorded on the network, and if more than an hour has passed, it is impossible to modify.
While this may disquiet some, it does mean that any transaction on the bitcoin network cannot be tampered with.
5 - Divisibility
The smallest unit of a bitcoin is called a satoshi. It is one hundred millionth of a bitcoin (0.00000001) - at today's prices, about one hundredth of a cent. This could conceivably enable microtransactions that traditional electronic money cannot.