MPPT stands for "Maximum Power-Point Transfer", and it is equivalent to two switching regulators back-to-back. It operates the solar panel at the load where the panel delivers it's maximum output power, then converts whatever Voltage this may be to a Voltage appropriate for the battery (depending on the battery's charge-state).
This is in contrast to the series-pass, Pulse-Width-Modulation (PWM), or shunt regulators. In these, the panel output is essentially connected directly to the battery during the charge-acceptance portion of the charge cycle, and the panel output is reduced once the battery approaches full-charge.
An example from my boat
: I have three BP 110W panels, wired in parallel. Each panel has an open-circuit (no-load) output Voltage of 21.7V (ratings at full noonday sun conditions, with a cell temperature of 25deg C). Each panel has a short-circuit current of 6.9A. The panel has a maximum output power of 110W, at 17.5V and 6.3A. At any other output Voltage the panel will deliver less than max power. When I am charging a low battery at (say) 12V, using a non-MPPT controller (or directly hooking the panel to the battery), the panel is not operating at maximum power. Looking at the output curve for the panel, at 12V the panel will be delivering about 6.8A, which is 81.6 W. (I am reading these Volt/Amp numbers from a chart in the panel specifications.)
With a MPPT controller, the panel would be operated at 17.5V, and be putting out 110W. Switching the 17.5V down to 12V (assuming 95% efficiency, a number I pulled out of the air) would give me 8.7 A into my 12V battery. This is a 28% increase in charging current.
Of course, the battery won't stay at 12V for long. As the battery Voltage rises, the current-boost will be less. At 13.5V, a directly-connected panel would deliver 6.75A (91W). With an MPPT controller the charge current (at 95% efficiency) would be 7.74A -- still one amp better.
Once the battery reaches full charge and the controller goes into trickle-mode, an MPPT controller will have no advantage.
These numbers will be different in practice, as the panels won't see constant full sun, and the panel temperature will usually be hotter. Still, the MPPT controller ought to give some charging improvement. MPPT controllers don't use fixed settings, but are constantly dithering the panel load, monitoring the panel Voltage, and looking for the point of maximum power.
These days, many panels are wired for 24V (instead of 12V) output, and the MPPT controller can efficiently convert the output of these panels for use in charging a 12V battery.
I still have the old-style controller for my panels, but I will probably be installing MPPT before too long. I may end up putting a seperate controller on each panel (instead of one controller driven by the three panels in parallel), because my panels are often partially shaded, and I think I will get more output if each panel can be independently optimized. I need to do some testing or modelling to be sure of this. I can't easily add more panels, so I need to make maximum use of the ones I have.
Hope this helps.