In America, palm leaves are popularly braided into crosses for Palm Sunday but are also braided into grasshoppers, birds, fish, flowers and other fun shapes. Other cultures use palm leaves to braid practical items, such as baskets, hats and food wrappers.
The Origami Resource Center website provides links to illustrations and instructions on how to braid palm leaves into crosses and various animals. The cross is one of the simpler crafts, requiring only a few folds to complete.
To make a cross, take a strip of palm leaf and make a diagonal fold at the middle of the strip so that the top part of the strip extends out to the right, then fold this strip over the center so it extends to the left. Fold this strip to the right again, but this time under the center. Take the bottom strip and fold it around the back and through the slot created at the center, this creates another slot in the center. Take the bottom strip again and pull it up through the bottom slot, then tuck the end of it into the top slot. Take the strip on the right and pull it through the right slot, then tuck it into the left slot to complete the cross.