In 13th Age, the icons are the setting's powerful non-player characters. They are not the Drizzt types who go off and have adventures at the expense of the player-characters, rather they are the rulers and wizards that send the player-characters on quests, or that send agents of their own to thwart them. An icon could be an end-of-campaign boss, or an ally against one.
Each player-character gets a number of relationship points to allocate to the various icons, so Alice of Zengis could have a two point relationship with the Dwarf King, for example. Each relationship is also defined as positive, ambiguous, or negative; if Alice's relationship with the Dwarf King is negative, it suggests that she hates dwarves, or he has betrayed her, or umpteen other potential disagreements.
For each relationship point a character has they get a six-sided relationship die; these are used in a number of ways but one of the more common is to determine which icons are going to be involved in that session's adventure. Everyone rolls their dice and each die that comes up as a 5 or 6 means that the relevant icon has taken an interest in events; a 6 means that the player-character will receive some sort of benefit from their relationship, while a 5 means that the benefit has some sort of cost.
The benefit could be something as prosaic as a bag of cash, or it could be something more narrative based; perhaps the wraith recognises the player-character as an agent of the Lich King and so lets him pass untouched and unleveldrained. Negative relationships tend to suggest that the benefit comes at a cost to the icon; Alice may use her Dwarf King 6 to recall that she knows a secret entrance into a dwarven fort, for example, allowing the party to bypass the guards. Ambiguous relationships could go either way, depending on context.
When I run 13th Age I tend to ask for these rolls at the end of a session so that I have some time to tie them into next week's adventuring, but the other day I wondered about using them at the start of a campaign; I was also thinking about die drop tables and the combination of the two trains of thought has resulted in this hideous chimera.
First of all grab a map from somewhere. You don't want too much detail, as the dice will be telling you where to put things.
Then each player -- or the GM on the player's behalf, but I think it would be more fun to involve the players -- takes it in turns to roll their relationship dice on the map. You want to know which dice are associated with each icon; roll them in separate chunks or use different colours, or something like that. Each die's final position determines a location associated with the relevant icon.
A 6 indicates that the location is some sort of stronghold of the icon. It could be a literal stronghold, or it could just be a town where everyone thinks the Crusader is a swell guy. A 5 suggests that while the place is associated with an icon, there's something else going on; perhaps the location is a new fortress and the local area has not yet been tamed. A roll of 1 to 4 indicates that the location is associated with the icon, but that there is little of campaign-level interest there, although something may come up in an individual adventure.
A negative die probably indicates that the location has been abandoned, or is in fact associated with one of that icon's enemies, or something like that. An ambiguous die suggests that the icon's control and influence over that location is not absolute; perhaps it's been conquered and the locals aren't too happy with the new regime.
Then you do the same again for the next icon.
If dice from two -- or more! -- separate icons share the same space then things get even more interesting. Perhaps that location is held in an alliance between two icons, or perhaps it's the site of a conflict between them. Maybe their forces are fighting a guerilla war in the streets of a ruined city, or the location is a dungeon into which both icons are sending adventurers to look for a great treasure.
Carry on until all the player-characters have rolled all their icon dice and you have something like this.
Bosh! There's your campaign map. You know where the major points of interest are, now it's time to tidy it up and expand as desired. If you started with a blank map, you could put forests wherever Druid or Elf Queen dice landed, or mountain ranges wherever the Dwarf King or Orc Lord dice fell.
Like the relationship dice themselves, this should be easy enough to use outside 13th Age; all you need to do is define your important factions and then give your players a number of points to spend on positive, negative, and ambiguous relationships with those factions. I suggest using at least seven icons so that there's plenty of potential for complexity.
As ever, if you do give this a try, let me know how you get on!