“Mods” fall into several categories, texture, vfx and animations. All mods are client side and as far as we know, are undetectable. Having said that, do not talk about mods in game but accept that there may come a time when all this fun stuff will end.
Mods can be installed and managed via Textools which is becoming obsolete https://www.ffxiv-textools.net/
The most encouraged method to install mods is using Penumbra. https://laillearda.com/penumbra
FFXIV Mods can be found at several locations:
Upcoming site tailored to the needs of the users and creators. If you have solid feedback and suggestions they will likely take it since the creator is not a Modder themselves.
Public Beta: https://heliosphere.app/
Mods downloaded from here utilize a plugin that downloads directly into penumbra and will support auto updating of mods.
The most well-known archive for mods but seems to be shrouded with drama as modders have opted to remove their work from it.
Stable modding community with a lot of paid mods and high-quality work.
Astral Oracles: https://www.astraloracles.com/
Aetherial Meadows: https://discord.gg/9N4c45rxwP
Keeping it simple, Body Replacement mods such as Bibo+ and Tight&Firm allow mod makers to design their outfits around a body shape, since ffxiv doesn’t really have one. These body replacements also involve higher quality skin textures and asymmetry. Bibo and Tight&Firm are the most common replacements. The biggest differences between the two are the shapes of body curves, how the body parts are put together and their respective agreements for using the body mod. You might find more paywalled mods behind Bibo+ though the body shapes are closer to vanilla.
If you aren’t sure which one to pick and you are only looking for compatibility for outfits then UNF3 is your safest bet since it contains materials for both Bibo and T&F3. If you are looking for T&F3 shape but with fixed Bibo materials, you can grab my version of the body mod here This is on Heliosphere so it required the respective plugin on the site for installing directly into Penumbra.