Chatter can happen to the best of us - Paul Sellers encounters it at 28mins 30 secs here planing the end-grain of a chunk of oak for a mallet head;
https://www.youtube.com/watch?v=u31Ixu6mSHY
The high-pitched squeal is very characteristic; he overcomes it here by skewing the plane to take a more slicing cut.
It happens when the flexibility of the thin blade allows the cutting tip to be driven backwards and slightly down into the wood, until the energy built up in the blade (which, being less than ideally clamped, acts like a flat spring) becomes enough to break the wood and spring the blade back to it's 'rest' position. The tip then digs in again, and the sme thing happens. The closeness of the resulting marks, and the pitch of the squeak, suggest that it happens quite a few times a second - something in the order of 50 to 100 times a second (or 50 - 100 Hertz, if you prefer).
You can demonstrate the blade flexibility to yourself with a six inch steel rule on the bench. Clear a patch of bench, and lay the rule flat on it, at right angles to the edge, hanging hole towards the middle of the bench, with about 10mm (3/8") overhanging the bench edge, which models the contact of the bevel heel with the frog. Put a thumb firmly onthe hanging-hole end, modelling the clamping of the lever-cap cam or screw. Now press down gently on the overhanging end, modelling the contact pressure of the cap-iron tip. You'll notice that the end deflects down a little, and the middle of the rule at about the 60mm (2 1/2") mark pops up off the bench. Pressing down harder (applying a cut) increases both deflections. Now, without removing your thumb, place a finger on the rule at about the 40mm (1 1/2") mark, and apply a little pressure to model the load applied by the lever-cap to the joint-line of a Stay-Set type or Bailey Patent type cap-iron. Now press down on the overhanging end again, and you'll notice that the same pressure causes much less downward deflection.
This is best done with a thin, flexible rule. If you try it with a thicker rule, you'll need a lot more force to get noticable deflections. That's exactly what happens with thicker plane irons - stiffness is proportional to the cube of blade thickness, so you don't need a great increase in thickness to improve stiffness a lot. Conversely, you don't need a great decrease in thickness to magnify problems significantly. That's why those using irons a bit thicker than factory standard experience chatter much less.
Those with thin irons can stop them acting like flat springs storing up energy by ensuring they're clamped better part way up the frog. That's why Stay-Sets and Bailey Patent cap-irons are good ways to cut down the possibility of chatter and generally improve plane performance by stiffening things up where it really matters - the bit that contacts and cuts the wood.