Isolation transformers:

One useful function of the transformer is that it can give isolation among the electronic circuits. While there is inductive coupling in the transformer, there is comparatively less capacitive coupling. The amount of capacitive coupling is reduced by using cores that minimize the number of wire turns required in the windings, and by keeping the windings distinct from one another (instead of overlapping).

Transformer coupling:

Transformers are at times used between amplifier stages in electronic equipment where a large amplification factor is required. There are other methods of coupling from one amplifier stage to the other, but transformers offer some advantages, particularly in radio frequency receivers and transmitters.

Part of the problem in bringing a radio to work is that the amplifiers should operate in a stable manner. If there is too large feedback, a series of amplifiers will oscillate, and this will degrade severely the performance of the radio. Transformers which minimize the capacitance between the amplifier stages, while still transferring the required signals, can help to prevent the oscillation.