After you install the package locally, you can find a package.json file inside node_modules folder. For example if you take file package you can find it locally at ./node_modules/file/package.json.
This file contains metadata of the package such as it's name, version, author, its git repository or homepage.
Also there is a package.json that could be inside application root. It describes a set of dependencies and scripts assiciated with it. When developers build an application, they create this file in root of the project.
This file, has the name and the version of the application, along with the list of dependencies what application requires or uses. These dependencies have also the corresponding versions of that it is used in project. Installing different or unsupported version of dependency - can cause application do not work properly.