Li-ion Battery charging process
It would be best if you did some web searching first to get a general feel for the subject and then you can ask more focused questions on areas that you still do not understand.

Look at www.battery university.com for answers to this and many othery battery questions.

BUT you will find that the "WHY" as opposed to the "you must do" is less well addressed in many cases. The following WHY / WHAT may be useful to more people than just you: 


  Why are constant current mode and constant voltage mode needed when charging Li-ion batteries?


Best answer is "because!" :-).
CC (constant current) is used when the battery will tolerate it for as long as it will tolerate it because that achieves about 70% to 80% of the charge as fast as is safish to do. CC rate is usually set at C/1 = current in mA = capacity in mAh numerically. IF you were able to safely keep charging at this rate the battery would be fully charged in just over 1 hour as they are 99% + charge current efficient.


  Why do we apply saturation charge even after the cell voltage reaches 4.2V?


When you charge from "flat" in CC mode the voltage starts off low (about 3V) and rises steadily if not quite linearly with time. However, and it is a very big however, once the terminal voltage reaches about 4.2V at about room temperature the voltage MUST NOT be allowed to rise higher. If Vbat gets to 4.3 V under C/1 charging it will probably "vent with flame" (something like a very slow explosion) and if it manages to get to 4.4V t more or less certainly will VWF and good luck on trying to get to 4.5V.

However - if you hold the voltage at 4.2V = CC mode the battery will slowly reduce the current it will accept and add about another 20% to the charge. People who do this do so because they want the extra 20% or so charge. As the current is continually decreasing this extra charge takes about 2 hours to add. When Ichg gets down to some preset % of Icc (maybe 50%, 25%, 10% if keen and silly, 5% if silly) charging is stopped. The lower you go the less extra you get AND the cycle life of the battery is reduced out of proportion to the extra capacity you get. If you keep doing this at 4.2V you may sooner or later get VWF as above or just damage the battery. Metallic Lithium is plated out of the cell structure and you really don't want that to happen. 


  What exactly is 'I-sense' in Li-ion Battery charging?


That one should be easy enough to search for yourself.