Android System WebView is a component of the Android Operating System and it handles tasks like displaying web content. This module is used by other application such as Chrome for example to load and display websites. It comes already installed on all Android devices and you should update this component only if you think it's urgent. Having the latest version installed brings more security and stability to your device when it comes to loading web pages.
If you develop applications for Android, WebView lets you add browser functionality to your app without having to code tons of lines. It is already used by many apps out there and you should not remove this library from your device.