Invasions, in New World, are events that occur when the Corrupted amass enough strength in a territory.
When this happens, an Invasion will occur, and they will attack the Fort, if the Fort falls, you’ll lose the battle. The higher level of the territory, the bigger the loss. When you lose, the Settlement will lose some, if not all, the upgrades built in it, and will have to be upgraded again. To participate in an Invasion, you can sign up at the Settlement’s Town Board, of which ten of those spots are reserved at the Governor’s discretion, whilst the other 40 spots are chosen randomly. Note, you have to be level 50 to participate in an Invasion. The Invasion itself has waves of enemies, and depending on how many waves you get through, you’ll be rewarded with EXP, Azoth, and Loot.
These are open world events that have portals across specific territories, these are small, but tough events which can yield good EXP and high-level rewards. They will appear with red skull icons on the world map, when you get to the location, you’ll have to fight elite enemies, then destroy the portal which spawns these abominations. If these are not taken out when they appear, they can lead to an Invasion (see above).