basket
籃 centers on a container made of woven material, specifically a basket.
籃 combines 竹 (bamboo) with 監, which likely contributes the sound ラン. The character originally referred to a bamboo basket.
The top 竹 is bamboo, and the bottom 監 looks like a container with a lid. Picture a woven bamboo basket with a sturdy frame.
For ラン, imagine a runner carrying a bamboo basket: run -> ラン, and the basket is made of bamboo.