What's the proper name for a layout like this, in which a column expands when mouse enters it: http://www.lucagiorcelli.it/test/volunia/
May be called "reactive layout"?
As mentioned by GotDibbs, this is an example of Progressive Disclosure. Although you are also partially correct in saying that it is a reactive layout. It's just that 'reactive layout' usually refers to the layout of the website changing on the fly to accommodate a smaller or larger area or screen size as apposed to the user interacting with individual elements.