Food
In the produce section of a grocery store, you will likely find very ripe coconuts. However, in tropical regions they are commonly eaten while the flesh is soft. Using a broken piece of hard coconut shell, you can scoop out the transparent sweet jelly and eat it as is. This jelly is what becomes the hard and white substance, or meat of the coconut. It is important to note that the heart of this palm is also quite edible.
Coconut milk can be a very important survival substance as well. It is sweet, watery and provides much needed electrolytes to the body. It also has more potassium than a banana. Survivors of a hurricane in Burma drank coconut water when no fresh could be found.
Shelter
Coconut palms have been called many things, including the "tree of life," as it is usable from the top to the bottom. If you are on a desert island, the second most important thing you are going to require is shelter. Palm fronds make excellent thatching material to block the sun's rays, keep you dry and provide matting for a survival type of bedding. Since you do not know what poisonous creatures may creep upon the ground, using palm fronds to make a hammock-like device is a good idea.
Utensils
As you can imagine, broken coconut shells can make instant bowls to eat or drink from, as well as viable storage containers. You can also use them for digging utensils if you want to hollow out a spot for your fire pit. Historically coconut shells have even been used as rescue tools. John F. Kennedy carved a message on a shell and sent it via natives to a naval base, effecting his and his men's rescue.
The veins of the palm frond can be bunched together to create a handy whisk broom, or used as individual toothpicks, should the situation call for them.
Miscellaneous Uses
Once you have shelter, food and a few utensils, you will be in much better shape to survive a desert island. Of course you may need a few more items such as toilet paper, fire starter and mosquito repellent, all of which can be had from the coconut palm.
*Toilet paper: tree wrapper.
*Fire starter: dried fronds or coconut husk.
*Mosquito repellent: smoke from burning husks.
If you have some basic tools with you, old coconut palm trees can also be used to build a sturdier structure. Old trunks of mature trees are often used as a source of lumber in tropical regions.