The Omen is a game mechanic that is used in all games of Eldritch Horror, represented by a circle in the top right corner of the map, with four circles inside.
The top circle contains a green comet, the bottom circle contains a red eclipse, and the left and right circles contain a constellation of blue stars.
Every game begins with the Omen marker on the green comet space, and it will rotate based on game and card effects. To "advance" the omen is to move the marker however many spaces are necessary in a clockwise manner.
Every time the Omen advances, any open gates must be checked. If the symbol on those gates is the same as the new Omen space, Doom advances by one space for each gate. If, for any reason, the Omen rotates counterclockwise, the same effect applies.
Some unique abilities allow the player to rotate or even place the Omen marker without advancing the Doom. This also applies to any non-Doom related effects.