The power in an electric circuit is equal to the voltage multiplied by the current. For a perfect transformer, all the power that enters comes back out. If the transformer is not perfect, a portion of the power that enters is converted to heat. The transformer is intended for use only with an alternating current while the current induced in the power lines as a result of space weather disturbances is a direct current. Magnetic flux ceases to be concentrated inside the iron core of the transformer and impinges on regions that were not designed to withstand this.
Power begins to be converted into heat.
The transformer moans and creaks loudly and overheats. Oil fires and melt-down of transformer components can occur. This happens not just to one transformer but at the same time to all affected transformers on the grid. Some transformers may burn up. Others experience significantly shortened lifetimes following damage during magnetic storm events but don't fail outright.