Cryptocurrency is a relatively new breed of digital asset where there is no central controlling authority. Cryptocurrencies use mathematics and cryptography to eliminate the need for centralized authorities.
Your regular bank account is essentially a digital ledger controlled by the institution you bank with. That ledger records how much you have on deposit, as well as any obligations like overdrafts, mortgages, or credit cards. The bank keeps a similar ledger for all of its customers.
In this case, you likely want the bank as a middleman to ensure that money is deducted from and credited to the correct accounts. You wouldn’t want every customer of the bank to have the ability to amend the bank’s ledger themselves, would you?
What Bitcoin achieved as the first cryptocurrency was the creation of a global, public, tamper-proof ledger with no central authority controlling it. The Bitcoin protocol is a ledger that everyone in the world can access, showing all the accounts on the network, how many bitcoins they control, and a set of rules about how many bitcoins exist, how many there will be, and how they are issued.
The true breakthrough of Bitcoin is that it solved a long-standing computer science problem: digital scarcity. From your experience in the digital world, you know that digital artifacts are not unique and can easily be copied. For example, when you send someone a photograph via email, you don’t lose the original; both you and the recipient have a copy.
Bitcoin’s clever mix of cryptography, mathematics, and incentives made it the first kind of digital good in history that is provably scarce and can’t be copied. This has opened the door for transferring value over the Internet in ways that weren't possible before.