Apoplexy is a now-dated term for what we now call a stroke, or the bleeding of an organ from hemorrhage. Both types of ailments were usually accompanied by a sudden loss of consciousness, as though the person was knocked out cold. So it makes sense that apoplexy derives from the Greek apoplēssein, from apo- ("completely") and plēssein ("to strike").
"'The governor is dying,' were the first words he said.
"'Impossible!' I cried. 'What is the matter?'
"'Apoplexy. Nervous shock, He's been on the verge all day. I doubt if we
shall find him alive.'
— Arthur Conan Doyle, "The Adventure of the 'Gloria Scott,'" 1893
Nowadays we are more likely to find apoplexy (or its adjectival form apoplectic) describing extreme or uncontrollable anger.