Committing this file to VC is important because it will cause anyone who sets up the project to use the exact same versions of the dependencies that you are using. Your CI server, production machines, other developers in your team, everything and everyone runs on the same dependencies, which mitigates the potential for bugs affecting only some parts of the deployments. Even if you develop alone, in six months when reinstalling the project you can feel confident the dependencies installed are still working even if your dependencies released many new versions since then. (See note below about using the update command.)
https://getcomposer.org/doc/01-basic-usage.md#commit-your-composer-lock-file-to-version-control