Trying to understand how a darlington transistor works
From my understanding the point of a darlington transistor is to take one voltage and boost it further than what a single transistor is capable of.


Incorrect. Bipolar junction transistors are current-gain amplifiers; for a given base current they allow a much larger collector current to flow. As such the first transistor amplifies its base current into a much larger collector current. This then becomes the base current for the second transistor which then further amplifies it, causing the overall current gain to easily reach over 500.