An anomaly is a feature of exploration in Stellaris. When a science ship scans a celestial body it may identify an anomaly that needs further investigation by the scientist on board. The higher the level of the scientist and the lower the level of the anomaly, the lower the odds of failure, which are visible to the player when deciding to investigate. Possible anomalies include mysterious obelisks, strange planetary features and ruins of alien civilizations, among many others.
Successfully investigating an anomaly will pop up an event than can give various bonuses, such as research points, resources on the planet, or even a Special project which requires further research investment to unlock benefits. The resulting project may be affected by species characteristics like Ethos: a spiritual species might worship an anomaly while a materialistic culture would offer a more scientific analysis for instance.
A failed investigation usually results in the anomaly vanishing, though it is also possible for the science ship to be destroyed in the process. In the worst outcome, the investigating scientist will also die.
As a result, leaving an anomaly for later investigation until you have more highly skilled scientists can be a wise move.