Why In an RF power amplifier, some output signal leaks back to the input through the device's internal capacitance (plate-to-grid in a tube, drain-to-gate in a FET). If that feedback arrives in phase with the input, the stage becomes an oscillator instead of an amplifier. Neutralizing means deliberately feeding back a small, equal-amplitude, out-of-phase sample from the output to cancel that internal feedback, so the stage amplifies only what you drive into it.
Watch out Keeping the carrier on frequency is the job of the oscillator/VFO stability and any PLL or crystal reference, not of the amplifier's neutralization network, though an unneutralized amplifier can certainly produce spurious signals.
Neutralize = cancel the sneak path. Amplifier that oscillates by itself needs out-of-phase feedback to shut it up.