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Exposure for the shadows is a mantra because you need a certain minimum amount of light to hit the film in order to get over the threshold where they will develop. The shadows areas on a negative receive the least amount of light from the scene and are closest to clear after development. In the attached diagram this is close to 1 on the relative log side of the graph.
Adjusting EI from 100 to 50 moves all your subject matter to the right. Shadow detail from the scene that may have been at 0.9 and not depicted on the negative at EI 100 may now be at 1.2 and visible at EI 50.
That doesn't mean it will print yet though. The area between the red lines represents what might straight print on grade 2 paper. (That is not actually a fixed area, it is controlled by enlarger exposure and paper grade. It is normal though to have preferred settings for printing that you target, so for this example I will assume the lines are that target.)
Lets follow the black line for a second. At about 1.3 on the relative log scale negative density reaches a point where it will stops printing black and starts printing shades of gray and at about 2.8 it reaches the point where it stops printing shades of gray and only paper white shows.
In this example your camera exposure has to be able to get the negative to 1.3 before the print will care.
You have to test for yourself to figure out where this point is for yourself.
As you can see from the three curves on the graph the bottom end is a bit like a hinge on a door, ISO and EI ratings are all basically ways to know where that hinge is.
The three curves represent changes to development (same exposure), blue is more development (N+), black is normal (N), green is less (N-). Notice that the hinge point doesn't change much. At this end of the scale exposure is king.
When you increase camera exposure all the subject matter moves right and following the curve. New subject matter rises out of the black past the lower red line into the printable area. The problem is though that at the upper red line highlight detail does the same thing moving up and out of the printable range.
Reducing negative development, green line, allows us to keep some of that highlight subject matter from moving out of the printable range. At this end of the scale development is king and provides real control.
Hence, expose for the shadows and develop for the highlights.
Even though this is quoted as mantra by many, it is a special case. It completely ignores any preferences we might have for say mid tone contrast. It's basis is sound but it's use must be tempered by experience.
The most usable portion of the saying is to expose for the shadows. If you don't reach the lower exposure threshold on the negative there is simply nothing there to develop.
