It's all about ground planes and differences in potential. A ground plane is the common wiring, which acts as "zero volts", and it not only includes the common ground on the circuitboard and from the power supply, but also the neg connector of the in/out jacks, and very often the metal housing of the pedal itself, as well as any metal knobs and switches. Because the jacks are part of this, the ground plane of any one pedal is also in common with the ground plane of any pedal it's connected to via patch cords. Additionally since you're using a daisy-chain supply, all the pedals have their grounds connected that way too. So it's a big messy loop, with every pedal affecting every other pedal.
"Potential" is a difference in voltage, so for example the only reason a circuit sees 5V at one component is because there is a 5V difference in potential between that part at that moment, and the ground plane. There's actually no such thing as zero V in a powered circuit--it's just a reference point.
When two devices are designed so their ground planes are not identical, there is a potential between those two planes--even though internally to each pedal the ground is "zero V"! When the is a difference in potential between two planes, there is voltage, and this voltage has nowhere to go, and it takes the path of least resistance, which very often means it leaks into the audio path as noise.
Even switching a pedal on and off can change the potentials, as the path of least resistance changes. So a pedal can be silent when "off" and noisy when "on", or the other way around!
And as often as not, the pedal that acts noisy isn't even the one with a problem. Just because the noise leaked into the audio path of pedal A, it could still have been pedal B that had the odd-man-out ground plane among the various pedals on the board.
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It's the daisy chain connections from the supply that complete the main loop through which the noise travels. Isolating the power for each pedal breaks that loop, reducing or eliminating the noise in most (not quite all) cases.
To be clear, it's not the wart itself that is "isolated", but rather the pedals that need their power isolated from other pedals. So you can do that by using batteries, or separate wall warts for the "problem" pedals, or buying a brick-shaped supply with isolated outputs like the Voodoo Labs PP2. Note the Dunlop Brick does NOT have isolated outs.