When you drag a file on to the Movies pane in Wii Transfer, the default choice is to prepare it for streaming. This will convert to Flash Video format and cache the file in /Users/your-user/Library/Caches/Wii Transfer/Converted Movies. When conversion finishes successfully, a "Show Movies Cache" button allows you to open the cache folder directly.
Wii Transfer does not automatically manage files in this folder. After converting many movies, you may need to clean up old files manually by dragging them to the Trash.
To watch movies, make sure the sharing checkbox is checked in the Sharing pane, then connect from your Nintendo Wii. Click on Movies from the main menu to see a list of converted movies, then click a movie to start playing it. The most recently 3 converted movies appear at the top of the list.
There is a quality preference for streaming movies in the Preferences window. After adjusting the quality, you will need to re-convert any existing movies that you want to watch with the new quality setting.
Learn more: Media Sharing, Network Setup.