to feed, to raise
餵 centers on providing nourishment and care to help something grow: feeding and raising animals or people.
餵 combines the food radical 飠 with 畏, which likely contributes a phonetic element. The character is not common in modern Japanese, and its exact historical development is uncertain.
The left side 飠 is food, and the right side 畏 looks like a person bending over to feed something. Picture someone carefully feeding and raising a small animal.
For ダイ, imagine feeding a pet and calling it to 'dine': dine -> ダイ, as you raise it with food.