the distributed ledger means that you don't have to trust anyone to perform a transaction. bitcoins act as digital bearer bonds in the same way that cash does in meatspace.
In addition I can securely store an encrypted file containing my private keys on several cloud services and access it from anywhere in the world. If done correctly, it is possible that no one knows that I have this asset until I try to cash it into a national currency.
That's just bitcoin itself. The bitcoin protocol opens up the possibility of all sorts of distributed and secure interactions, contracts or property titles for example. namecoin is a distributed DNS service based on this idea.
