Why a stabilizer
Fluctuations in the voltage are quite common and are possible for many reasons so it is hard to keep them all in check which is why a stabilizer is of great use. The main function of a stabilizer is to make sure the voltage is as close to a fixed value as possible so the equipment being powered isn't affected so if a surge is headed to your premises it will be absorbed before it hits your electronic devices. If there is high-performance equipment like in hospitals or data centers this is a crucial need as voltage fluctuations in those spaces could have a lot more drastic damage, so a stabilizer will make up for the voltage variations on the mainline.
How they work and power ratings
The stabilizer manages fixed voltage values using circuitry which changes taps on a built-in autotransformer, along with the help of quality electromagnetic relays. To pick what power rating you need your stabilizer to be you need to calculate what all load it will be picking up and leave about 20% space for more. This extra 20% would work for homes but maybe not for factories or larger consumption systems so there your safety margin should definitely be higher. So for instance at home, if your stabilizer will be looking after equipment consuming around 1000 Watts then you can take a 1200 VA or 1.2 kVA stabilizer.
There are stabilizers that are built for specific equipment as well like for ACs or refrigerators, they are engineered to be working with just that device alone and won't be taking anything else on. It is a good investment if you want to protect your electronics in the house or other places.