Why do Ethereum addresses work on Polygon and Binance Smart Chain? 

If you create an Ethereum address in your wallet (for example MetaMask), the same address can be used on other EVM compatible layer 2 chains, such as Polygon Matic and Binance Smart Chain. 

The reason is because these sidechains use the same digital signing algorithm and blockchain address derivation function.  It's like creating a bank account number at one bank, and finding that the same account number now exists and can be used in other banks in other countries. 

Perhaps the catchphrase "be your own bank" should be changed to "be your own banks"...