To keep it simple, warehouse is a new feature that lets you store items in an invisible giant warehouse so that you can retrieve them anywhere in the world without needing to go to a chest.
It also has the ability to keep items on you (or take them automatically). So for example if you're mining it can automatically take the Cobble from your inventory and store it in your Warehouse while making sure you always have 16 torches in your inventory etc
Below are the commands, when you see something in < > it means that is required, when you see things in [ ] that means it's optional.
Manually Storing Items:
/store [quantity] - Store the item in your hand in the optional quantity you specify (if you don't provide a quantity it will just store what's in your hand)
/store all - Store every one of this item that you're holding
/store inv - Store everything in your entire inventory (except enchanted things, renamed things etc - It ignores those)
(If you supply a username like above it will store the items in that users warehouse instead of your own. So for example instead of doing /store 12 you could do /store _Pri 12 to send Pri the 12 items you're holding instead.)
Manually Retrieving Items:
/get <name> [quantity] - Retrieve or just view the quantity stored of the item you specify by name, if no quantity is specified it will try to give you upto 1 full stack of that item when you click on it in the menu.
/get list - View a list of everything you have stored (warning list could be huge!)
Automatic Inventory Management:
/auto [Quantity] [verbose] - The quantity you write here will be how much the Warehouse tries to keep in your inventory at all times (it checks your inventory once every 30 seconds). - If you include the verbose (like /auto 12 verbose) it will send you a message when it alters your inventory. This can be useful if you want it to tell you when it moves diamonds or other valuables etc
/auto off - Disable the auto you've setup for the item you're holding
/auto list - View and remove (by clicking) any auto's you have setup.
So for example if you write /auto 0 while holding Cobble it will try to make sure you have 0 cobble in your inventory at all times, anything over that amount it will take from you and store in your warehouse.
Similarly if you want always to have 64 torches on you (for mining etc) you can hold a torch in your hand and type /auto 64 - Any torches above this amount will be put in your storage and any below that amount will be given to you from your storage to keep your total at 64 in your inventory.