Remember, TS never injects polyfills in your code. It’s not its goal. Complementing the accepted anwer:
target tells TS which ES specification you want the final/transpiled code to support. If you configure it as ES5, TS will down compile the syntactic features to ES5, so any arrow functions () => {} in your code will be transformed to function () {}.
Whatever you choose for target affects the default value of lib which in turn tells TS what type definitions to include in your project. If you have "target": "es5", the default value of lib will be ["dom", "es5", "ScriptHost"]. It’s assuming which functional features the browser will support at runtime. Adding things to lib it’s just to make TS happy – you still need to import the polyfill yourself in the project.
So in short: configure target first, and if you need any extra polyfill in your project OR you know your browser(s) will support this little extra feature, lib is how to make TS happy about it.
Example:
You need to support IE11 but also you would like to use promises. IE11 supports ES5, but promises is an ES6 feature. You import a promises polyfill, but TS is still giving an error. Now you just need to tell TypeScript that your code will target ES5 and it’s safe to use promises in the codebase:
"target": "es5",
"lib": ["dom", "es5", "ScriptHost", "es2015.promise"]