How to fix faulty 3dm file?

 From:  Brian (BWTR)
1604.8 In reply to 1604.7 
"any time that you just sort of free-form position 2 pieces nearby each other without a snap"

Sorry, right there, I am lost.(Thinking back, I can not think of a logical step I took incorrectly from what I have learnt/done previously?)

Could you please diagramatically detail the difference betwen the two. What I did wrong and what I should have done!