The "front end" circuits of radios amplify small signals, which are basically varying electric fields. Because signal strengths can vary depending upon a number of factors in the environment surrounding the radio antenna, they incorporate what is called automatic gain control, or AGC, which varies the amplification of the received signal in order to produce a nearly constant level of signal to the following stages of the radio. Otherwise, the volume of sound that you listen to would irregularly be going loud and soft.
High tension power lines produce an electromagnetic field that surrounds them. If the radio is close by, that field can be so large that even with very selective tuning in the radio's front-end, enough power from that power line signal can get through to the AGC that it thinks there is a very strong radio station signal. It clamps down on the amplification, so the actual radio signal is then "lost" in the background noise that is mostly the 60Hz field from the power wires.
