I'm playing the Special Edition Version of Skyrim on PC, so the mods I'm linking to are the mods compatible with that version of the game.
Most important and the first mod anyone should install is the Skyrim Script Extender. It's a mod that creates an alternate executable file for the game that gives the player, as well as external files and applications, access to Console Commands and script editing. Most mods other than the simplest mods on PC need this to work.
To install, select the appropriate file form the link I gave you, and download the file. Next move the file to your Skyrim folder on you PC (usually found under Program Files (x86)/Steam/steamapps/common, I would show a screenshot, but my Skyrim folder is installed in a different location to the default) then using an archive access app, such as 7-Zip, extract the folder into your Skyrim folder.
Once that's done, your Skyrim folder should look something like this;
As the cursors tell you, you now have a different .exe file to use to start the game. In that screenshot there is also a shortcut I created to that file that I eventfully copied to my desktop, a good thing to do to ensure so you don't get the Script Extender executable file mixed up with the standard one.
The next thing you need to do is download the Vortex Mod Manager and create an account to start using nexus mods. The process is fairly straight forward and there's plenty of tips and videos online to help tech yourself how to use VMM, but I'll obviously help out as best I can if you need help with a specific problem.
We (The VGR community) will obviously be try to assist yourself and anyone else as best we can with trying to install mods, so feel free to ask any and all questions you have. There are no stupid questions nor problem too small.
Now onto the question you asked about the images. The first image is of a player home mod called Sjel Blad Castle and it's pretty self explanatory, It's a massive, beautiful fully equiped and furnished player home complete with followers, displays and convenience features such as a teleport system to help you move around the place and an auto-sort system for you inventory.
The others are just an illustration of some of the enhanced visuals mods I've installed. They basically replace some of the textures and effects that are in the game with other textures and effects created by other people other than the game dev's. A mixture of Realistic Lighting, Realistic Water, This Cites overhaul, This OTHER Cities overhaul, 3D Trees and Plants, Trees in Cities and a Flora Overhaul. They may be more at work than just those, but those are some of the good ones. I've installed other mods to improve the gameplay and immersion such as Rich Merchants so one doesn't have to wonder to town after town to sell of swag, a First Person Perspective overhaul that has the actions as they are in third person mode display in first person (This mod is great, but it does take some getting used to as by default the primary weapon is on the left with secondary on the right, but while dual wielding as I like to do, the weapons look like they've swapped around) mods that add Better NPC AI, Better Follower AI, more Jewellery, Weapons and Armour options to the game.
There's other things like new followers, questlines, character creation mods and alternate face/body textures, but let's not get ahead of ourselves, I think I may have offered enough for now. Like i said previously, please ask if there's something you want to know