OK, found this schematic, which is reasonably easy to understand.

The collector-emitter voltage drives the top half of the coil. Note that the emitter is AC coupled to the center tap.
The feedback into the base of the transistor is taken from the bottom half of the coil.
When the top of coil swings positive with respect to the center tap, the bottom of the coil swings negative ( again with respect to the center tap ). This is due to the coupling between the top half and bottom half of the coil.
But the collector-emitter voltage swings opposite to the base drive ( more base current = more collector current, so the collector-emitter voltage is lower ).
So the net effect is positive feedback. The circuit "wants" to oscillate.
But you cut the gain by adjusting R2 so that it doesn't quite oscillate.