Anomalies are oddities picked up by shipboard sensors that warrant closer investigation. These are almost always optional and bear little impact on main objectives, but these usually yield resources, items, or new missions/assignments.
Maps on uncharted worlds have little initial information. Anomalies are denoted by question marks and later marked X upon exploration.
Mass Effect 2
If a planet or moon has an anomaly, EDI reports detecting one once the Normandy SR-2 enters planetary (or lunar) orbit. Actively scanning the celestial body is required to locate the source of the anomaly.
The targeting reticle contains a white line pointing in the direction of the anomaly during scan. When the targeting reticle gets sufficiently close to the source of the anomaly a white dot will appear on the map marking the anomaly's location. Launching a probe towards the white dot unlocks the assignment, and allows landing on the anomalous world.
Anomalies generally produce a radio chatter that gets clearer and more distinct as the reticule approaches the anomaly. The exception are the anomalies introduced with the Firewalker Pack, which are completely silent.
List of Places with Anomalies
Mass Effect 3
As before, EDI announces if she has detected anomalies. The presence of anomalies usually indicate Search and Rescue retrievables like fuel, War Assets, or intel, although they may yield waypoints for certain missions.