At any of the Local Storage locations, you can store excess items. Everyone gets 5 spaces, free of charge. If you wish to have more space than this, click the "Storage Options" button to see the available storage packages. One you set up a Camp, you will have access to the items of the local storage there, too. It requires a house of size two to upgrade the local storage the first time. After that, further upgrades may be done with houswe sizes of four, six, eight and ten.
Once your clan has got a fort, this location also offers access to a storage. Note that this storage is not shared with the local one, meaning that you also have to control the upgrades separately. These depend on the forts size in a quite similar way as the local storage depends on the house size.