Wow this is an amazing question that is really and interesting one to think and research. 

Normally all the trees are made of wood. I mean the body is fully wood made. But if you cut a palm tree then you will see that the whole body is a combination of scattered fibers that are spongy and attached with each other like they are set with glue. This spongy tissues are the main source of flexibility of a palm tree. Because of this flexibility palm tree can lean down to the ground with the force of wind and than come back to the position again. That's why palm tree can survive even from the hurricane. 

Another reason is palm tree have a huge number of small roots on the upper part pf the ground which make a huge anchor with the lower parts roots by holding a lot of soil to make a strong base. That's why palm tree doesn't come out from the soil even in extreme windy condition. The upper part of the tree is also very flexible and the leaves are like feathers. So small amount of wind can stay there which is harmless. Most amount of winds are actually pass through the gap. That's why branches are also stay secured. Also the cylindrical shape of palm tree is technically a super aerodynamic structure to stay safe from wind. 

This is not only for palm trees but also in case of coconut trees. Thanks for reading.