Cryptocurrencies are digital monetary units. In contrast to fiat money such as the Euro or US-Dollar, produced by central banks, this currency is generated by a network.
The cryptos are in the direct possession of the respective person. This eliminates the need for intermediaries, similar to banks and current bank accounts.
Like the Euro notes in your wallet, digital money is stored in an electronic wallet. And just like with cash, you can take your wallet with you anywhere, including abroad.
However, much like a real wallet, it might be misplaced. Access requires a form of a password known as a "private key". If the owner loses this key, neither he nor anyone else can access the money.