A Chest is a pretty simple item which can be placed on the ground after being built. The chest will then allow you to store up to 9 stacks of items in it which can be very useful. However once placed the chest can't be moved and it can catch on fire resulting in the cooking or destruction of its contents.
The main appeal is that it keeps your items organized and keeps them safe from the elements, particularly wandering hungry animals. Because it can be used to hold your valuables, it is generally a good idea to also build a Lightning Rod to protect it from lightning strikes that can start a fire and destroy it.
Aside from just holding items that you don't immediately need, it's also good for storing an extra set of items or holding items in remote locations that you may need. For instance, you could build and place one near a Touchstone filled with warm clothing so that if you are revived during the winter, you won't instantly freeze.