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.
Though this term doesn't seem to be used by Thomson Reuters, I agree with Sh. Arun Inamadar above.
Where h-index and i10 index shows relationship between published papers and cited papers, the so called cumulative impact factor of an individual shows quality of such publications and the number of citations they can attract.