Cryptography & Blockchain
If two or more people want to securely transact over the internet proving their identity they can make use of asymmetric cryptography or public-private key cryptography where each of them holds a private key and a public key.
The purpose of using public-private key cryptography for the Bitcoin blockchain is to create a secure digital identity reference. The combination of these keys creates a digital signature. It is used in blockchain to prove ownership of your assets and control your funds. The Identity of a wallet holder is therefore based on possession of a combination of private and public cryptographic keys.
A Bitcoin or any other cryptocurrency wallet does not store any coins, only the public-private key pair associated with your bitcoin address. It simply acts as secure key storage, and as a communication tool with the blockchain.