The implication here is that they die while living their life as usual, and not of old age and being bedridden with illness, infirmity, etc.
The "Die with your boots on" idiom originates from frontier towns in the 19th-century American West.
[1] Some sources (e.g., American Heritage Dictionary of Idioms) say that the phrase probably originally alluded to soldiers who died on active duty.
The Oxford Dictionary of Idioms says: "Die with your boots on was apparently first used in the late 19th century of deaths of cowboys and others in the American West who were killed in gun battles or hanged."
Cassell's Dictionary of Slang adds that from the late 17th century until the early 19th century the expression meant "to be hanged", and from the mid 17th century until the mid 19th century "Die in one's shoes" meant the same thing.