The game is an MMORPG closer to WoW than your other mentioned games. Players are organized into Guilds/Clans known as "Free Companies" and can only be in one free company at a time on a character.
Playing together members can run about in the open world doing Treasure Maps, Hunts, and "FATEs" although not many people do FATEs anymore, 4 player dungeons, 8-Player "Trials" and Raids, and 24 Player "Alliance Raids". Players can also work towards getting a Free Company House and decorating it as they see fit. There are also a variety of other activities players can partake in as well.
Parties are typically made up of 1 Tank, 1 Healer, 2 DPS for "light parties" in dungeons, and 2 Tanks, 2 Healers and 4 DPS for Trials and Raids. The interesting thing with FFXIV is you can play every single class on a single character, so there's no real need to create separate characters.