From Gods and Icons:
When a player rolls a 5 on their icon relationship roll, they get a complication. Sure, the icon will help them out, but something else happens to make the story more interesting.
Here's an example from Gods and Icons. Instead of rolling dice, for this example we'll have you scan the tables and pick a fun complication.
The players are outside the Espairian Empire in the city state of Paxbellum (substitute place names from your own world). The drow paladin in the party rolls a 5 with his positive relationship with Tanadil, High Queen of the Fey (see her preview here, or substitute with an icon from your own world).
You're in town, not a dungeon, so you look at the social complications. You scan down and pick
A local power is opposed to the icon. Embarrass them at an upcoming social event. Sabotage the event.
That sounds fun. Who's opposed to Tanadil? You could pick King Thorbal of the dwarves, but you've been hinting that Emperor Roland wants to take the city state into his empire, so you pick locals working for the emperor.
You can down to the local power table, and pick a member of the ruling council. She's setting up the event to advance the emperor's agenda.
Then down to the event. You scan down this list and hit on a public feast, commoners invited.
So that's your complication, Tanadil wants the PC to disrupt a feast where the commoners are being fed by the largess of the emperor. Make the emperor's toadys look bad. You decide councilwoman Chale calls it the "Friendship Feast" and invites one of the emperor's numerous bastards to speak at it.
Now it's up to the PCs. Who doesn't want to make some lord high muckty-mucks look bad?