The blockchain technology can solve many problems. It's a decentralised, immutable, trustless ledger (database)... There are tons of scenario's that pop to mind, basically any scenario where equal partners want to create a database between them, but don't fully trust one partner to run a classical database out of fear this one partner that hosts the db would tamper with the data.

You can use a blockchain database to store insurance information and share it between insurance companies and individuals; univeristy's can use it to store hashes of grades, titles, diploma's, so somebody interviewing for a job can immediately be crosschecked about the diploma's he/she claims to have;... and those are just 2 commonly known examples.

For bitcoin, the blockchain technology solves, amongst other things, the double spending problem. By storing transactions onto a decentral, trustless, immutable ledger, people can not double spend unspent outputs without their transactions getting rejected (given that the first transaction is already included in a block at the time the double spending transaction is broadcasted).

Even the people that hate crypto currencies see the potential behind the blockchain technology