The Deno REPL is a tool you start by typing 'deno' in your terminal. Once started, you can type JavaScript or TypeScript code and press Enter. If you define a variable like 'let x = 5;', the REPL shows 'undefined' because declarations do not return a value. When you type an expression like 'x * 2', the REPL evaluates it and shows the result, here '10'. You can also run commands like 'console.log("Hi")' which prints 'Hi' and then shows 'undefined'. To exit the REPL, press Ctrl+C twice. This interactive environment helps you quickly test and learn code snippets.