Hi Peter welcome to the forums.
QUOTE:
It might just be me, but I cannot get that part around my head? As I read it, I am supposed to install my compiled file that I just downloaded from my source site via the component installer on my destination site?
Yes that is correct.
When you press the compile buttons at the top Export Content collects the sections or static items you have selected and builds a component that can be installed on any other site where Export Content is setup.
As to the error you are receiving it may be because there is a character that the site installer has run into that it can't parse.
What versions of Export Content do you have installed?
Export Content version 1.7.0 should be on Joomla 1.0+ series
Export Content version 2.0.0 should be on Joomla 1.5+ series
Export Content version 1.0.0 is for Mambo.
In your situation you should have version 1.7.0 installed on both the source and destination sites.
So if this is how you have things setup and are receiving the above error try compiling a few items at a time to see if you can isolate the item that is causing the problem.
Is all content in English as the Joomla installer will choke on some characters?