[bmcusick]

The blockchain is an accounting ledger that no one has global write-access to, so you don't have to worry about your bank/broker being hacked, going out of business, or freezing your accounts.

It solves the problem of financial intermediation. The whole financial world has been built on financial intermediaries (banks and stock exchanges) to verify that you actually own things. Now you can point to a public record (the blockchain) for that, and no one can take it away from you (without your private key).