Climax originates from Greek word κλίμακα (climaka means ladder). It has several definition in English. I copy from dictionary.com
noun
- the highest or most intense point in the development or resolution of something; culmination:
- (in a dramatic or literary work) a decisive moment that is of maximum intensity or is a major turning point in a plot.
- Rhetoric
figure consisting of a series of related ideas so arranged that each surpasses the preceding in force or intensity
the last term or member of this figure. - an orgasm
- Ecology. the stable and self-perpetuating end stage in the ecological succession or evolution of a plant and animal community.
verb
to bring to or reach a climax.
So the word originates from word ladder in Greek but kept the metaphorical meaning of the word. That something escalates until goes to the highest step of the ladder. Even the word escalates originates from the latin word for ladder scala that it is mostly used and in modern Greek.