Making coffee is all about extraction. The compounds you find in coffee beans that add flavor dissolve at different moments of the process. Some dissolve almost instantly when the coffee grounds come in contact with water. Like for example caffein and the more acidic compounds. Others take a while before the water dissolves them, like bitter compounds and sugars. The goal is to have an even extraction. To get the best possible flavor out of the coffee. You want some sugars in there to give it sweetness, but you don't want too much bitterness. You want fruitiness and acidity, but you don't want it as sour as lemon juice. So you need to balance the extraction.
There are different variables influencing this process, but they all come down to how fast and much extraction is happening. The grind size, the water temperature (and mineral content) and the brewing time just to name the most important ones.
Wetting the grounds, or blooming, is preparing them for the extraction. When coffee is roasted CO2 gas is trapped inside the beans. Wetting the grounds, without water passing through the filter (for drip coffee where blooming is most important, certainly more than for full immersion techniques like French press) has the effect of the CO2 being released to ensure an even extraction when you are brewing. There are several straight forward reasons for that and some more technical ones.
Blooming prevents channeling of the water (the phenomena that all the water will flow through small holes of grounds instead of saturating all of them)
If you don't bloom the gas in the beans will bubble upwards pushing the water away from the grounds which results in channeling and uneven extraction of the particles that are trapped inside the gas bubbles.
Imagine your grind, it's made up of particles of different sizes with most of them somewhere hovering around the size you actually wanted. So when you start pouring water without blooming the small particles will soak up the water faster than the bigger ones and will obviously start extracting earlier. In the end that will result in over extracted small particles and very under extracted bigger particles. By pre infusing the grounds you even that out a little bit. By adding just enough water to infuse all of the grounds without already extracting, you start from a more even level. The smaller particles will still extract more than the bigger ones, but the extraction levels are evened out, because the starting point is more leveled and extraction begins at the same moment for all grounds.
"Why should I pour remaining water in batches anyway?"
This is more a matter of style. Some Baristi prefer it that way and others pour continuously. More important is that you don't brew excessively long or short. Between 2,5 min. and 3 min. is a good time (for Hario V60, different for other pour over methods). Some say that pouring in batches helps being consistent, but it's not something that's necessary. I brew very consistent (measurably with a refractometer that measures total dissolved solids or TDS) and I pour continuously.