Using the Package Manager
Having clicked to open the asset in Unity, you will see a floating window that looks similar to this:
Don't worry if it looks a bit different or if it's docked instead of floating. If it says Package Manager on the top tab you are in the right place.
A package is a digital container that holds any combination of assets, shaders, textures, plug-ins, icons, and scripts. (So basically, anything Unity can handle.) Unity has a number of 'official' packages that come with the editor. The assets you get in the Asset Store come in their own packages. You can even create your own packages to share. The Package Manager helps you deal with all this awesomeness. You can see everything available and what, in particular, has already been installed in your project. It also allows you to install new packages, update existing ones, and remove those you don't need.
If you want...