I'm not a pro player so there are some higher tier strategies & tactics that I'm not intimately familiar with. However this is my basic understanding of it:
The shape of the map, the lanes, and the positioning of the objectives are all interconnected. For example - Why are there 2 Champs on each side in the bottom lane (in most mid-elo "meta" games) instead of 2 at top? Because Dragon is an early objective that a team needs to control, so having 2 Champions there gives the team greater "Dragon control" - you can pull your mid laner and jungler in and have 4 Champs to either take or contest dragon, instead of 3 if you only have 1 laner at bot.
The Jungler can also benefit from one side or the other. If you are a jungler who starts at the Gromp (the frog, and usually goes to take the Ancient Golem buff next) then it is usually an advantage to be on Red Side because your 2 bot laners can easily help leash or damage the Gromp to help you clear faster. If your jungler starts at Krugs (to then take the red buff) they usually benefit from Blue Side because, again, your bot laners can help you. 2 helps are better than 1.
When I jungle it also usually determines who I'm going to gank first. If I am Blue Side, and I start at Blue Buff, I'll probably have to go back and recall instead of ganking after my first set of camps. That means that my first gank will come after I take Red Buff. That means I'm more likely to gank mid or bot lane, since I'm already on that side of the map. If I know that I really want to gank top lane (say they have a Nasus and I want to camp him) I might try to start red instead so that my second clear will be at blue buff and I can immediately run to top lane and gank.
What about bot ganks? At bot lane, the position of the bushes can make it easier or harder to gank. Tri-Bush is often a highly contested area to ward because if the Blue Side bot lane is pushed, a jungler can easily flank them from the tri-bush instead of river, catching them between the 2 laners and the jungler. So Blue Side wants to ward it & the river if they're going to push up. Red side, on the other hand, can usually ward just the river bush and the lane bush and be pretty safe even if they're fairly pushed forward (all of this depending on the Jungler. Junglers like Rek'Sai or Zac can come at you from anywhere)
Also Dragon is on the Blue Side of the river, meaning that if Red Side is trying to take Dragon they run the risk of the other team either jumping over the wall into Dragon Pit or trying to steal it from that direction, which is why Red Side teams will usually ward over the wall behind the dragon pit.
These are all just a few examples but there is actually a ton of depth into the specific placement of every piece of terrain in League. Try to figure out, for example, why they changed the top lane bush from 2 bushes (like bot lane has) and instead has 3 smaller bushes. Think about how it changes ganks (such as the jungler trying to "lane gank" from a bush)
