A memory foam mattress consists of a top layer of temperature
sensitive memory foam and other layers of different foam underneath
(the foam base). Some manufacturers use convoluted foam, others high
resilliance polyurethane foam, etc.

I want to know what exactly in the foam base influences the overall
quality and lifespan of the mattress (type of foam? density of foam?
resilliance? durability? lifespan?) and how that translates to me, the
customer. In other words, what makes a great foam base in a memory
foam mattress?

The best base for a memory foam mattress is a LX hospital grade base. 
Some companies use an HR or high resilience foam for a base, but it
won't last as long as an LX base.  An LX base is used by Tempurpedic,
which is the pioneer in memory foam sleeping surfaces.  My company
also uses an LX base on most of our mattresses.  It provides a longer
lasting solid support for a memory foam mattress.  In the meantime you
can get a ton of information at http://www.memoryfoamfurniture.com.