Try to make them smaller, and the shadows blur into a hazy gray that is useless. If someone figures out how to create a sharper picture of the circuit, that immediately opens the door to faster computer chips and memory chips as well as hard disks that hold more data. The phase-shift in the masks adjusts light waves so that the blur into the dark region between two features cancels each other out giving true dark regions. Consider two neighboring holes in the chrome mask. Because light travels slower in glass than in air, creating a trench in one of the holes causes the light waves to exit this hole with less phase delay than the other.
Light waves consist of oscillating magnetic and electric fields.
When one light wave's electric field is up, the other is down. When the blur contributions meet in the middle region, they add up to zero. The result is a darker region to separate the features. Of course, it's not quite that simple in the real world. They solve in detail how light moves in and about the phase-shifted masks.