Locksmith here.
In a standard household lock, there are usually 5 chambers that hold 5 sets of a top and bottom pin. When the key enters the lock, it raises these sets of pins to each particular height so that the space between the top and bottom pin lines up with the turnable part of the lock (the shear line). If even one of those sets doesn’t line up properly, the lock cannot turn.
A master keyed lock works by having a top, bottom AND middle pin in at least one chamber. This makes two different lines in the chamber. Meaning 2 different keys can raise the pin to 2 appropriate heights, since there are two spaces.
A master (or middle) pin in all five chambers exponentially increases the number of different keys that will work in each lock, though it is still common practice to have all three pins in each chamber, even if you only want one extra key to work.
Determine master key possibilities, numbers etc gets a bit complicated and requires above an ELI5.
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