LarsG,
COM (aka ActiveX) is Microsoft's Common Object Model. It enables Windows applications to make Components available to any language with Com support.
For example, when you use WebGadget, you are really using a component exposed by Internet Explorer via COM. If you look in the helpfile for the WebGadget you'll see that it explains that ActiveX is used. Activex is COM, it was just rebranded by Microsoft to compete better against Java.
Read more here:
http://www.wikipedia.org/wiki/ActiveX
DX refers to Direct X. Direct X is Microsoft's multimedia library that gives low level, 'bare metal' access to the graphics hardware.
The DirectX API is exposed through COM, rather than the old-style Windows API dll calls that PureBasic already supports.
Native COM support will give the native access to the API, so you are no longer dependent upon the subset of features supported by the PureLibraries.
More about Direct X here:
http://www.wikipedia.org/wiki/DirectX