Legend - Green area is total number of unique, active addresses used per day; Blue line is annual % change in address count:
address growth explained
Addresses in the blockchain world are kind of like bank accounts. But not really that much. Like bank accounts, blockchain addresses are controlled and used by individuals. Individuals can use these addresses as unique "identifiers," like bank accounts, allowing them to send and receive payments to third parties.
The similarities pretty much stop there.
Unlike bank accounts, addresses on the blockchain can be generated by anyone, anywhere. No one's permission is required to create an address. No one's permission is required to send cryptocurrency across the blockchain, in amounts too big or too small. The biggest risk the user must think about is the control and security of their "private keys," which are somewhat like randomly generated passwords, allowing for access to funds in their addresses, or "accounts." Third parties and other hardware devices have made this process much smoother over the years, and it will continue to get smoother.
And of course, as has been noted elsewhere, these projects don't just stop at payments. Ethereum's blockchain, for example, specializes in "smart contracts," which allow users to communicate, interact, and do business with each other in many ways beyond payments.
The charts above graph various blockchains' growth of addresses which are both unique and active, smoothed out over 10-days for easier reading.