Pellet stoves keep a stock of compressed wood or recycled pellets in a hopper. The hopper continually adds new pellets to the combustion chamber as the stove burns. This a real but clean-burning flame with concentrated heat. Pellet stoves can be very efficient, but low-frequency noises are common in most units. Sometimes these noises indicate problems with the system, but usually they are simply signs of stove operation.
Pellet stoves are known to produce low rumbling or humming sounds as they burn as part of their normal function. This is a product of the low-exhaust operation of some pellet stoves and cannot be stopped. The rumbling simply means the pellet stove is on and burning. It should not correspond with any changes in burning efficiency or loss of air flow.
It is likely that the low-frequency noise you hear is there to stay -- unless you want to upgrade to a new pellet stove. There are higher-end pellet stove models that specialize in quiet furnaces that deaden the noise. These furnaces may cost more, but can help reduce nuisance noise if you have your stove installed in a family room or bedroom where the rumbling can be distracting.
If the rumbling is not coming from the combustion chamber it may be originating in the pellet stove's blower. These blower helps cycle air around the firebox to heat rooms more effectively. But a low droning or buzzing noise can indicate fan problems. The blower may have become slightly loose, so it now produces vibration, which stops if you can reach and tighten any loose bolts.
If your pellet stove was once quiet but is now producing an unexpected low, rumbling noise, shut down the stove and try to find the source of the noise. A clogged air supply vent is often responsible and may need to be cleared. A dirty firebox or hopper can also cause a change in noise. These problems can be fixed (usually with cleaning) to restore normal operations.