The diode at the gate (or the gate-channel diode in a JFET) rectifies your oscillation signal amplitude and charges the series capacitor so that the gate will be negative. The larger the amplitude is, the more negative the gate gets, and the drain current gets smaller. This is the AGC which keeps the signal reasonably clean.
The trick is from the tube era. A grid-dip meter functions by measuring the grid/gate voltage by measuring the current in the grid resistor.