What keeps the leaves alive?

My Pepper cuttings usually take at least one month to root, but the leaves that I keep always thrive.  I've recently thought  about this when I took a cutting from a plant that hadn't been watered for a while and the leaves were very droopy.  Once a put a cutting from the plant in water, they perked up almost instantly.  It is obvious that the stem absorbs the water and transplants it to the leaves.  I'm just curious as to how all of this works  What is the process called?  
 
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