Cryptocurrency, or crypto for short, is a relatively new breed of digital asset where there is no central controlling authority. Unlike traditional currencies that are issued by central banks, and are controlled by the banking system, cryptocurrencies use mathematics and cryptography to do away with centralised authorities.
Your regular bank account is essentially a digital ledger controlled by the institution you bank with. That ledger includes how much you have on deposit with that organisation, as well as any obligations, for example, overdrafts, mortgages, or credit cards. The bank in question keeps a similar ledger for all the rest of its customers. So, if you instruct it to send some money to your aunt, the amount gets deducted from your bank account and credited to hers.
Now, in this case, you may want the bank as a middleman to ensure that the money is deducted from and credited to the right accounts. You wouldn’t want to trust every customer of the bank to be able to go in and amend the bank’s ledger on their own, would you?
What bitcoin achieved as the first cryptocurrency, was the creation of a global, public, tamper proof ledger, with no central authority to control it. So, the bitcoin protocol is basically a ledger that everyone in the world has access to, showing all the accounts on the network and how many bitcoins they control, as well as a collection of rules regarding how many bitcoins there are, how many there will be, and how they are to be issued.
But the true magic of bitcoin is that it solved a long-standing computer science problem, that of digital scarcity. You know very well from your own experience in the digital world that digital artifacts are not unique and are incredibly easy to copy. If you send someone a photograph via email, this doesn’t take the image off your own machine and deliver it to them, you keep a copy and they get one too.
This problem is partly why every industry that has entered the digital world (publishing, music, film) has had to change business models, because as soon as their products were made digital, they were easy to copy and distribute without having to pay for them.
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.