1.) The concept of public and private is to create a safe and secure digital signature. The computer takes you wallet and randomly generate a private key. This number is so astronomical that it most likely won’t be generated more than once. A mathematic function is then used using the private key, to create a public key which is used to create a public address. This is a secure address to send and receive transactions.
2.) The two key use cases for public key cryptography are in cryptocurrency are encryption, and creating digital signatures.