incense tripod
鼐 refers to a large, three-legged incense tripod used in ancient rituals. Its meaning is specific to this ceremonial vessel.
鼐 combines 乃 (top) and 鼎 (bottom). 鼎 is a pictograph of a tripod vessel, and 乃 may have contributed a phonetic element, though the exact historical development is uncertain.
The bottom component 鼎 looks like a tripod vessel with legs and a body. The top 乃 can be imagined as curling incense smoke rising from the tripod, making 鼐 an incense tripod.
For ダイ, picture a large incense tripod standing on a dais: dais -> ダイ, and the tripod sits on the dais during the ceremony.