The Log Window is a scrollable window which contains technical output which the MacRTrace ray tracing kernel generates during the scene reading, enclosing and rendering. It looks like this:
 
The log window is limited to 1000 lines of text. After this limit is exceeded, the oldest lines will disappear from the top. If you want to see a complete, unlimited log of the rendering, look at RTrace Log File, which MacRTrace creates in its directory each time it is launched.