(n): an event that occurs at a critical time
(n): the decisive moment in a novel or play
(n): a particular point in time
(n): the moment of most intense pleasure in sexual intercourse
(n): the act of bringing to completion or fruition
(n): the most severe stage of a disease
(n): a specific identifiable position in a continuum or series or especially in a process
(n): arrangement of clauses in ascending order of forcefulness
(n): a use of language that creates a literary effect (but often without regard for literal significance)
(v): end, especially to reach a final or climactic stage
(v): have an end, in a temporal, spatial, or quantitative sense; either spatial or metaphorical
Climax is derived from the Greek word for 'ladder'. And there's more history at the OUP blog.
Further research shows that there are also towns named Climax in Michigan, North Carolina, Georgia, Pennsylvania, Saskatchewan and Minnesota. The last is just down the road from Fertile, MN ... hence the famous newspaper headline about a fatal car accident: "Fertile Woman Dies in Climax".
A ghost town in Colorado, USA. There is no truth in the rumours that it was recently purchased by uselessness.
Climax was once the highest settlement in the USA. The town was effectively closed down when the molybdenum deposits were worked out.