A spatial anomaly was a thing in space that wasn't supposed to be there. It made it hard for ships to go. Sometimes, a ship in space would have to look for things to make it go. But then the ship would go, and everybody would be happy, at least until next week.
In 2153 the NX-01 was subjected to damaging anomalies within the Delphic Expanse (Space Pirates of the Expanse: Curse of the Big Sphere). These anomalies were later discovered to have been generated by enormous, millenia old Spheres as part of a plan orchestrated by the Sphere Builders to reconfigure the Expanse, making it a habitable region of space for their species, the prelude to an invasion stopped in the future by the Federation.
The effects of Spatial Anomalies could be countered by insulating the hull with the compound Trellium D, this substance however might cause any and all Vulcans onboard to become overpowered with emotions and go murderously insane (ENT:Impulse).