When some plants are at the end of their lives, bout to die, they employ all of there
energy to one last burst of life, usually resulting in the rapid emergence of some
sort of colorful, large and remarkable flowering.
What is the botanical/biological term for that?

Are you thinking of monocarpic or semelparous or hapaxanthic? Like Bambusa
or Agave?

Monocarpic is the term usually used for plants; semelparous for animals
(e.g., salmon); hapaxanthic is usually used for palms and bamboos.

Kay