I will try an over- simplification, and I mean really simplified.
If you could ring your barrel as it is mounted in the rifle stock it would sound like a tuning fork. If you where to shine a high frequency strobe light on the end you would see the muzzle sweeping back and forth in a pattern that resembles a daisy. The nodes are the points in the motion where the muzzle sweeps through the center (focus) of the "daisy", that is, where the muzzle would be at rest.
When you shoot the bullet has a certain amount of barrel time and exits the barrel as the muzzle sweeps somewhere around the "daisy" pattern. If it is exiting as the muzzle approaches the out edge of the "daisy pattern" (here to for referred to as the 'DP') it will be aimed with maximum deflection of the muzzle. But here is the key: that maximum deflection may be at 3 o'clock this shot, 7 o'clock next shot and maybe 10 o'clock the next. The barrel does not traverse the 'DP' in the same pattern for every shot.
Now for the nodes. As you change velocity, up or down, the barrel time changes. As the velocity/ barrel time coincides with the "node" of the muzzle sweeping through the at-rest center/ focus of the 'DP' the bullets, at that narrow range of velocities, are exiting the muzzle when it is in the only common point of its travel around the 'DP'. The center is the geometrical focus of the pattern the barrel is vibrating/ringing through. Although the bullets may vary slightly in velocity (and barrel time) from shot to shot, the muzzle will be at a very small deflection from center/ focus and tosses the bullets to nearly the same place. We call that "accuracy".
In a ladder test, as you increase the powder and the velocity the bullet's POI changes on target. As the barrel/ bullet combination reaches a "node" increasing powder charges/ velocity start grouping together. The bullets quit stringing. As you pass through the node the bullet impact will begin stringing out again.
That is why the ladder test is important. If your load is shooting in the middle of a node, small variations do not have as great a detrimental effect on the accuracy of the rifle.
Now if I could just find a "node" for my shooting skills.....