Back in the days of yore (that is, before you could make waveforms bend over backwards at the touch of a button), an echo chamber was a cheap and effective way to add an echo to an audio source. The chamber consisted of a room (though there are portable versions) made of a sound reflective material with non-parallel walls. A speaker was built into one end and a microphone was built into the other; a sound played through the speaker would bounce around the room, fragmenting as it went, and would then be picked up by the microphone along with its echo.
Some of the smaller models were configurable - the angles the sides of the box made with the ends could be changed to alter the characteristics of the output. The effect was most frequently used to add menace to the sound of footsteps or to make a voice sound ghost-like, though the chambers had applications on the music side of the fence as well.
Nowadays synthesizers and computers do all the work, but there's a certain appeal to the old fashioned method - the particular sonic characteristics of audio piped through an echo chamber is (along with the theremin) one of the major hallmarks of mid-twentieth century radio.
More colloquially, an echo chamber is any forum where a pundit is assured the lack of a dissenting opinion or criticism. Certain poetry communities on LiveJournal, for instance, seem to operate under the 'if you don't have anything good to say, don't say anything at all' philosophy, which feels great for the author in the moment and does absolutely nothing to make them a better writer. The radio programs of Certain Extremist political commentators and slashdot are all, to greater and lesser extents, echo chambers.
Alternately, as Simpleton points out, the term can refer to the bouncing of a sound bite between different media organizations until it gains a sort of momentum of its own.