Could someone tell me why Flash Player needs
ttf-mscorefonts to work?
In Flash IDE, when creating a text field, there are two options in terms of specifying a font:
if a "normal" font is selected (i.e. Ubuntu or Droid or Comic Sans), outlines of the symbols used will be included in the swf file as vector shapes, so the text will be displayed identically on any platform
there are also some special fonts: _sans, _serif and _monospace - when those are chosen, the outlines are not included in the file and Flash Player uses system fonts instead. Which, on Windows, are Times New Roman, Arial and Courier New.
Because Flash movies are authored predominantly on Windows, they're tested with those fonts present. I don't know if there's a hard dependency built into Flash player, but even if not, some/many movies will be displayed incorrectly if those fonts are missing.