The word east comes from Middle English est, from Old English ēast, which itself comes from the Proto-Germanic *aus-to- or *austra- "east, toward the sunrise", from Proto-Indo-European *aus- "to shine," or "dawn".
This is similar to Old High German *ōstar "to the east", Latin aurora "dawn", and Greek ēōs or heōs.
Ēostre, a Germanic goddess of dawn, might have been a personification of both dawn and the cardinal points.