A.k.a. “core saturation.” A condition where a transformer’s core is fully magnetized and is producing maximum magnetic flux. This typically happens when the transformer is not large enough for the application. While some players feel core saturation affects the sustain and distortion an amp produces, it can have an adverse affect on tone, reducing bass and dulling highs. Core saturation can also increase the temperature of the transformer and the amp’s tubes. How/when a transformer saturates is a complex topic, dependent on many factors within an amplifier design.
There are very few amps or amp makers that rely on core saturation for tonal enhancement, though transformer or core saturation is a factor in the distinctive tone created by “tweed” amps when they are cranked up.