What happens during the charging process is this:
During charging, an external electrical power source (the charging circuit) applies an over-voltage (a higher voltage than the battery produces, of the same polarity), forcing a charging current to flow within the battery from the positive to the negative electrode, i.e. in the reverse direction of a discharge current under normal conditions.
What that means is that when you charge a lithium-ion battery the charger forces charge to flow from the positive to the negative electrode, reversing the process of discharge. Once that happens, your battery is charged. A diagram below shows the discharge process, which is the reverse of charging:
Now for your more specific questions:
- The constant current is to keep the battery's current at the proper level. As the battery's voltage is increasing from charging its current would decrease without constant current.
- Saturation charge is basically adjusts the battery's current to the level the battery is rated for.
- I-sense is current sense.
Hope this helps!