Dont understand represent what,and over what?
As disparate as those moments were, for each of these six people they" represented "a crossing over,' passage to a place from which there will never be a return. Such changes, of course — multiplied by millions of lives — are also transforming their homelands, the greater Middle East and, by inevitable extension, the entire world.

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It means: "[meeting the ISIS gunmen] represented a jump/a bridge/ a passage to a place etc." (I read the full sentence in the article)

Crossing over = http://www.dictionary.com/browse/crossing--over (Have a look at the examples)

Let's see what natives will say. :)

Answer

There are some punctuation mistakes and there is a missing "a" before passage.  This makes it hard to understand the meaning quickly.
they = the moments.  
represent = symbolise.  
Manuela has given you a good link.