dawn, daybreak, clear, explicit
曉 centers on the first light of day: dawn or daybreak. The extended senses of clear and explicit grow naturally from the idea of things becoming visible and distinct as light arrives.
曉 combines 日 (sun) with 堯, which likely contributes the sound and the idea of high or prominent, suggesting the sun rising prominently at dawn.
The sun 日 rises beside 堯, a shape associated with height. Picture the sun climbing high at dawn, making everything clear and explicit.
For キョウ, imagine the dawn light shining on a 今日 (きょう, today) sign: 今日 -> キョウ, and the new day begins.