There are a lot of good reasons for the inverter-controlled motors in HVACR. Let me mention a few here, hopefully without putting you to sleep.
They increase system efficiency and offer greater comfort control, such as, by allowing high efficiency modulating gas furnaces to more closely match the heating loads and to equalize the temperature in a building with lower fan speeds between heating cycles. High efficiency 13 SEER and up indoor evaporator AC coils are larger than older 10 SEER coils. Because of the larger surface area and shorter system run times etc., they don’t remove humidity at the same rate as the older coils, so the indoor blower unit is sometimes run at lower speeds to help control humidity levels in the building, even when the T-stat is satisfied. Most older indoor units just used standard 2-speed motors, high speed for cooling and low for heating. The inverter controlled DC motors allow for almost infinite speed control. Many companies like Mitsubishi and Panasonic are using them for condenser fans and for compressors to match BTU output to the cooling load.
If you really want to learn more, you can visit another website where I am a member: http://www.hvac-talk.com/
It’s a pro only site and no DYI info, but there are general discussion forums you can search through or join if you want to post questions. Just like here on ECN, if you ask questions, you will get excellent answers.