a type of bamboo, round bamboo lunchbox
簟 refers to a specific type of bamboo and, by extension, a round bamboo lunchbox made from it. The meaning is narrow and concrete, centered on this particular bamboo product.
簟 combines 竹 (bamboo) with 覃, which likely provides the sound. The character originally referred to a bamboo mat or utensil, consistent with the bamboo-related meanings.
The top 竹 is bamboo, and the bottom 覃 looks like a container with a lid. Picture a round bamboo lunchbox made from woven bamboo strips.
For タン, imagine a tan-colored bamboo lunchbox: tan -> タン, and the box is made of bamboo.