Transpiling is the process of interpreting certain programming languages and translating it to a specific target language. In this context, transpiling will take compile-to-JS languages and translate them into the target language of Javascript.
Transpiling is the process of converting source code to source code, and this is a common activity in JavaScript development.
The features available in common JavaScript applications (Chrome, Firefox, NodeJS, etc.) often lag behind the latest ECMAScript specifications (ES6/ES2015, ES7/ES2016, etc.). Once a specification has been approved, it will most certainly be available natively in future versions of JavaScript applications.
Rather than waiting for new JavaScript releases, engineers can start writing code that will run natively in the future (future-proofing) by using a compiler to convert code written for newer specifications into code compatible with existing applications. Common transpilers include Babel and Google Traceur.
Transpilers can also be used to convert from another language like TypeScript or CoffeeScript to regular, "vanilla" JavaScript. In this case, transpiling converts from one language to a different language.