1680s, "the histories of individual lives, as a branch of literature," probably from Medieval Latin biographia, from later Greek biographia "description of life" (which was not in classical Greek, bios alone being the word there for it), from Greek bios "life" (from PIE root *gwei- "to live") + graphia "record, account" (see -graphy).
The meaning "a history of some one person's life" is from 1791. The meaning "life course of any living being" is by 1854. No one-word verb form has become common; biographise/biographize (1800), biography (1844), biograph (1849) have been tried.
compound adjectival word-forming element, usually interchangeable with -ic but sometimes with specialized sense (such as historic/historical, politic/political), Middle English, from Late Latin -icalis, from Latin -icus + -alis (see -al (1)). Probably it was needed because the forms in -ic often took on a noun sense (for example physic). Forms in -ical tend to be attested earlier in English than their twins in -ic.