Baskets have been made and used since ancient times. They were traditionally made of thin, flexible twigs. Willow twigs were ideal for this and used for thousands of years. Thin strips of cane were also used.
A basket is open weave, and usually of a stiff material. That is what makes it different from a bag, which is close woven from a flexible material such as hemp.
Baskets today can be made from plastic strips. We also call wire shopping carriers baskets, although they are not woven.
Making baskets is a skilled craft.