These are the three categories a Weekend Challenge entry can fall into. Non competing ones are entries which (for all kinds of different reasons) will not be included in the voting. Only pure and open entries will be added to that list on Monday evening.
The general rules of the challenge are outlined here: Welcome to the Weekend Challenges
Or in short: If you can honestly say to yourself, “Yes, I mainly used Blender to make this”, “Yes, nearly all of the foreground models are new”, “Yes, most of the models are new”, then the entry is Pure. (I like to read “foreground models” as “important parts of the entry”.)
And last but not least: All competing entries which are not pure, are called open. 
One word of caution: The rules have been written down roughly 500 years ago and I really should try to find the time to make a few adjustments. Some parts are ‘a little’ outdated and some parts aren’t all that clear. There have been quite a few discussions on that matter. For clarification I and others have written down some thoughts about this: Challenge #889 Voting CLOSED - #12 by Helge
I hope this helps!