An Icon is a powerful NPC that has a strong influence on the world, both within your campaign and milieu that the players are not interacting with. Icons may aid our oppose the player characters over the course of the campaign, and the player's selection of icons at the start of play will actually shape the direction that the campaign will take. If no one has put any points into having a relationship with the Great Gold Wyrm and all characters have a relationship with the Dwarf King then you should expect that icon to be more relevant as play goes on.
As you can see in the chart above, there are forms that relationships can take; positive, conflicted, and negative. At character creation you have three points to spend on relationships with the various icons. At the beginning of play you roll one die per point you have spent and there is either no effect, a positive result, or an ambiguous result that contains both advantages and disadvantages for the character.
So, as a brief example, let us say that a player rolled and got an ambiguous result with the heroic icon named Archmage. During play the character may receive aid from the Archmage's organization, but has drawn attention from the Diabolist who attempts to oppose the player character with her cultist minions.
This system is designed for a very broad campaign setting, but could be easily applied to a megadungeon and its surroundings by replacing very general archetypal icons with the major players within the megadungeon region. There could be icons representing the less alien factions within the megadungeon, but also icons representing factions around the megadungeon such as the bandit lord or the swamp witch. This allows the Dungeon Master to develop some major factions in the setting but gives the players some say in what factions they are interested in interacting with.