From Latin 'geniālis' (of one's guardian spirit) — in Roman belief, genial warmth was the radiance of one's inborn protective genius.
Friendly, cheerful, and warm in disposition; conducive to growth or comfort.
From Latin 'geniālis' meaning 'of or belonging to the genius, festive, joyful, pleasant,' derived from 'genius' (innate spirit, guardian deity, natural talent), itself from the verb 'gignere' (to beget, produce). The Latin traces back to Proto-Italic *genos and ultimately to PIE *ǵenh₁- (to produce, to beget, to give birth). This root is one of the most productive in Indo-European, yielding Greek γένος (génos, race, kind), Sanskrit
Every Roman had a 'genius' — a personal guardian spirit born with them and responsible for their vitality and character. 'Genial' behavior was literally 'genius-inspired' behavior — the warmth and festivity that your inborn spirit naturally produced. Birthday celebrations were festivals honoring one's genius.