How does the pressure change in the Air Cycle Machine? In this picture:


#3 says:


  "Air expanding to ambient pressure turns expansion turbine, is greatly cooled, and drives compressor." 


I understand all of that except for the "air expanding to ambient pressure" part.

Ambient means relating to immediate surroundings of something so the pressure can change. I understand that if it decreases in size like at #1 it would get hotter or if it increases in size it would become colder, but how can it be ambient if all the air is expanding to the same size when at #3 the column that the air passes through doesn't change shape to change the pressure? 

Basically, how can it be ambient pressure if the column doesn't change size?
Strictly speaking you're right, the authors used a brief and easy to visualise but slightly inaccurate phrasing. The blue bit is open to the cabin, and at the end of it will have cabin ambient pressure. At the beginning of it the pressure will be slightly higher, but very much lower than before the turbine.

The pipe diametre does not need to change for the pressure to vary. Air streams from high pressure to low pressure, upstream pressure will always be higher than downstream pressure, by an amount to overcome the friction forces.