Mac Mini to Apple TV
You don't mention which AppleTV you own, so I am going to assume that it's the currently available model, or at least generation, because it's probably more likely, and its easier to answer :)

The answer it that you cannot move stuff onto the AppleTV, it's a streaming only solution.  Whilst it has a small amount of internal storage (I think 4Gb for the 1st version of the 2nd Gen model that I have) this is used to buffer streaming, particularly for movie rentals from iTunes etc.

So to simply view, rather than move, content that is held on your Mac Mini, or any device come to that, is to ensure that it is playable in a player that offers the chance to use AirPlay to wirelessly stream the content.  You'll need to be on the same LAN as the AppleTV to see the device, but assuming you are you should simply see it as an output source when you click the AirPlay symbol in the player.