Questions concerning Solar MPPT tracker
The point of MPPT (maximum power point tracking) is to continuously adjust the load presented to the solar array for maximum possible power transfer.  The output voltage from the solar array is affected by the current - if the current is too high, the voltage will drop and if the current is too low, then the voltage will saturate.  This is represented by the I-V characteristic of the solar array, and it varies with temperature and illumination.  

Basically, the way this works is the input resistance of the controller is adjusted such that the product of the voltage and current (power) drawn from the panels is the largest.  The controller is generally configured in a similar manner to a buck DC to DC converter, and the duty cycle of the switching transistor is adjusted to change the current draw from the array.  The voltage and current from the array are monitored by the controller, and the duty cycle (current draw) is adjusted to keep the efficiency high.  According to https://en.wikipedia.org/wiki/Maximum_power_point_tracking , there seem to be several different methods of doing this.  The simplest method is called 'perturb and observe', and the idea is to adjust the operating point slightly and then check to see if the new operating point is better or worse than the old one.  

One possible problem with MPPT is that the output power will vary continuously, therefore it is necessary to have some sort of load-smoothing capability in order to fully utilize the power from the array.  Generally this is done with a large battery bank.  The batteries will be charged from the array with varying charge current as the power from the array fluctuates, ensuring that the maximum amount of power from the array can be captured.  

Partial shading is where some parts of the solar array are in shade and as a result perform differently.  MPPT controllers connected to the entire array cannot compensate for this, and the efficiency will suffer.  MPPT controllers connected to individual panels can track the best power point on each panel individually and can compensate for partial shading to some degree.