lift, raise, open
撬 centers on using a tool or lever to lift, raise, or pry something open. The meanings all involve applying force to move or open something upward.
撬 combines 扌 (hand) with 毳, which likely contributes the sound. The character suggests using the hand to lift or pry, but the exact historical development is uncertain.
The hand radical 扌 is using a tool to lift the heavy, bristly 毳 object. Imagine prying open a crate with a crowbar.
For キョウ, imagine using a lever to lift a heavy object while shouting 'kyo!' with effort: kyo -> キョウ.