understand, comprehend
懂 centers on mental clarity: understanding and comprehending something fully.
懂 combines 忄 (heart/mind) with 董, which likely contributes the sound and may be related to directing or managing, suggesting mental direction toward understanding.
The heart/mind radical 忄 beside 董 (which looks like a heavy weight 重 under a plant 艹) suggests the mind working to lift a heavy idea into clarity: understanding.
For トウ, imagine a toe tapping as the mind finally comprehends a difficult concept: toe -> トウ, and the understanding clicks into place.