Each mystery box costs 15 FarmVille cash. They are sort of expensive, but you have a chance to get a variety of items (you will get at least one item) in addition to some experience points.
To buy them, click on the mystery box icon at the top left of the screen:

This will open up the menu and you can purchase them there. Here is what the in-game text says for the mystery box:

To purchase one, click the "Buy" button then place it on your farm. To get the items, click on the crate and then click the "open" tab. I ended up buying one and here is what I got:
Red Bike & 30 XP
Here are a list of drops:
Red Bike and 30 XP
Firepit and 80 XP
Lawn Chair 50 XPCountry Picnic Table and 60 XP
Striped Rest Tent and 60 XP

Tree Swing and 150 XP

Gold Gnome and 200 XP
Hot Tub 200 XPThese things really seem to be worthless unless you specifically want one of the decorations, which means you are going to have to spend a lot of FarmVille cash to get it. Otherwise, the XP / coin reward seems to be very low to me for the cost. For example, the giant spider web (Halloween limited edition decoration) costs 30 FarmVille cash and gives 600 xp when placed. That's a lot more XP per farm cash than getting even the best crate outcome!

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