Possibly a variation of Hebrew Ayelet, meaning 'doe' or 'gazelle of the dawn'.
Ailet is usually read as a Hebrew-leaning name, most likely a variation of Ayelet, the word for a doe or gazelle, sometimes expanded in poetic use as the gazelle of the dawn. That gives it a delicate natural image at the core, with the kind of soft, luminous feeling that many Hebrew names carry.
In modern use, Ailet feels rare and understated rather than familiar. It has the lightness of a nature name, but it is not generic or obvious, which gives it quiet distinction. The name sounds airy and graceful, and its biblical-adjacent background helps it feel rooted even when it appears in contemporary style.