What is Cumulative Impact Index of a journal?
The term "Cumulative Impact Factor" (or cumulative impact index) has been used with different meanings by different authors.  

One definition is that the cumulative impact factor for an individual author is simply the sum over all papers that the author has published of the impact factors of the journals that the papers were published in.  e.g. 

You've published 3 papers in Journal A that has impact factor 1.2.
You've published 1 paper in journal B that has impact factor 1.9.
You've published 2 papers in journal C that has impact factor 1.7.

Your CIF would then be 

CIF=3*1.2+1*1.9+2*1.7=8.9

Like all bibliometrics, it's a very crude measure.   You can get a high score on this measure by publishing a lot of research in journals that aren't very prestigious, or by publishing a very small amount in highly prestigious journals.  

Furthermore, the metric says nothing about the impact of your research compared with other papers in the journals in which you've published (e.g. you might have published a very widely cited paper in a journal with a low impact factor but you won't get any extra credit for that.)  

The term "cumulative impact factor" has also been used for measures of the impact factor of a journal over extended periods beyond the usual definition of impact factor.  See for example:

http://www.garfield.library.upenn.edu/papers/impactofcumimpfacs.pdf

I don't believe that ISI has ever defined this term in their formal reports on the impact factors of journals, so I'm afraid that any use of the term will depend on the particular group or person that is computing the cumulative impact factor.