A MPPT or Maximum Power Point Tracking charge controller is basically a charge controller that has a buck-boost power supply inside of it.
A system using an MPPT charge controller will usually be designed with a much higher solar panel system voltage than a traditional charge controller system will or can use. This means that the wires/cables can be thinner because the amps carried will be lower (the wattage stays the same) an this higher voltage also means that there will be more voltage generated by the solar panel system even when the light is not optimal, and will allow the MPPT charge controller to provide charging capacity under less than ideal conditions.
What it is able to do is to convert excess voltage coming from the solar panels into usable charging current or power. A traditional charge controller effectively uses resistance (or pulse modulation) to reduce any excess voltage coming from the solar panels to a safe voltage for the battery bank, but the excess voltage is converter into heat or otherwise wasted (not used to charge the batteries).
The MPPT charge controller usually can operate lighting conditions that result in voltages that are "low" or "lower" and boost it up or convert it to a usable charging voltage, so that the power from the solar panels can be used for charging, the current (amps) will drop, but this is much better than no or zero charging that a traditional charge controller will do under the same conditions. This means that an MPPT charge controller will continue to work and will send power to the batteries even when it's cloudy, and is able to start charging earlier in the morning and till later in the evening than a traditional charge controller can or will.
That this simply means that an MPPT charge controller will put more power into the battery bank under many conditions that a traditional charge controller cannot. And even a small charging rate is "better" than no or zero charging rate. This benefit is mainly due to the design/redesign of the solar panel system to have a higher initial voltage, but can even make a difference even when using solar panel system that was originally designed to be used with traditional charge controllers. MPPT charge controllers can be "dropped" into an existing system and it will effectively make the solar panel system "bigger" or more "efficient" by providing more charging power over a longer period of time, which means that there will be more power available to use, well, that is as long as it is used by the load when the battery bank is full.