Anomalies are opportunities for you to earn skill neurons, which allow you to level your commander’s skills. You can access anomalies by completing Chapter 2 (Orion Clouds), stage 5 of the campaign.
Each anomaly is associated with a specific affinity and is color-coded accordingly. To see your commander's affinity, go to the hangar and tap on the commander, or observe the color of their level label, as highlighted in orange below. The higher the level of the anomaly, the rarer the skill neurons; rarer skill neurons can be used on higher rarity commanders. Click here for more information about skills.
To enter an Anomaly, select the "Battle" button on the main menu and tap "Anomaly" on the interface.