Perhaps this blurb from a manufacturer sums it up more concisely: they say the signal is tranferred "via electromagnetic induction" and creates "power transfer without distortion"
Audio transformers are typically composed of copper wire windings around a steel or nickel-iron alloy core. Each core material transmits electromagnetic signals differently. Steel has a higher degree of hysteresis (magnetic signal lag), making it better for lower frequency transfer. The higher permeability of nickel makes it ideal for transmitting higher frequencies.
The windings around the core determine the impedance level, which increases, decreases, or maintains the signal level as it passes through the transformer. When the signal enters the transformer via the input (primary winding), it then gets transferred to the secondary winding via electromagnetic induction. More windings around the core correspond with a higher impedance, so if the primary winding has more than the secondary, the signal will decrease (step down). Conversely, if the secondary winding’s impedance is greater than the primary, the signal will increase (step up).
Impedance matching is one of the primary uses of audio transformers. Impedance is determined by the efficiency of the conversion from voltage into magnetic flux. In addition to stepping signals up or down, audio transformers can match the input and output impedance levels to create efficient power transfer without distortion or signal overload. Impedance-matching transformers will not necessarily boost or attenuate the signal but will create balance for an optimal energy transfer.
From:
Understanding Audio Transformers | Triad Magnetics