The current edition of ECMAScript (ES5) is the one that is widely accepted among all well-known browsers. You can think of it as the traditional JavaScript; whatever code is written in ES5 can be executed directly in the browsers. The problem is that most modern JavaScript frameworks contain features that require more than the traditional JavaScript capabilities. That is the reason ES6 was introduced. With this edition, and any future ECMAScript editions, we will be able to empower JavaScript with the features we need.
Now, the challenge is in running the new code in the current browsers. Most browsers nowadays recognize standard JavaScript codes only. So, we need a mediator to transform ES6 to ES5. That mediator is called a transpiler and the technical term for transformations is transpiling. There are many good transpilers out there and you are free to choose whatever you feel comfortable with.
Tip
Apart from TypeScript, you might want to consider Babel (babeljs.io) as your main transpiler.
Google originally planned to use AtScript to implement Angular; later they joined forces with Microsoft and introduced TypeScript as the official transpiler for Angular.
The following figure summarizes the relationship between various editions of ECMAScript, AtScript, and TypeScript.
Note
For more details about JavaScript, ECMAScript, and how they evolved during the past decade, visit https://en.wikipedia.org/wiki/ECMAScript.