>What problem / which problems are being solved here?

Lets say I want to transfer some assets to a guy without anyone knowing from any internet connection. There is a demand for this global service.

Crypto-currency faciliates this. You buy crypto with your normal currency. Transfer. Switch back to normal currency. Yes you've endured some volatility in price but the whole operation was done in an hour or so.

So legit business will set up as "Bitcoin Banks" allowing people to trade in and out of them.

It's truly "digital cash".