Ambient declaration files are just another .d.ts file, but they don't define any import or export. Remember back to when we discovered excluding import and export creates a "global" module. It's the same for .d.ts files, so if we omit import and export from the top level we can use it to document globals using the TypeScript type system.
This is actually how lib.d.ts works! Using the same concept, the community is able to maintain type definitions for other modules or environments, such as node.d.ts. You just have to be aware that any type information you put in this file will be global to your project.
Occasionally you do need to write your own global typings for things that weren't included using TypeScript's lib.d.ts or the community maintained definitions. In this case, you can create your own file (I recommend globals.d.ts) and reference it using files in tsconfig.json. Now you're types will work perfectly.
Of course, the final use-case for ambient declarations is third-party module typings. There's over 200,000 modules on NPM! That's a lot to type. Let's just implement the type definition for something simple, like arrify.d.ts.
Using declare module "name" creates that modules typings within the current project. It allows us to import name later on, which turns out to be a huge part of NodeJS development, or anyone using CommonJS for that fact.