Your inventory (or backpack) is where all of your items are stored. This screen also allows you to equip items. The inventory can be accessed by pressing "B", or by pressing escape and locating the button that looks like a backpack, as shown below.
There are several ways to equip an item, all ways to equip items require the mouse to be held over the item in the inventory. After you have moused over the item you wish to equip, and have checked that your class can use such item, and that your power level meets or exceeds that of which is required; right click to equip. You can also middle mouse click to equip or hold down left mouse button and drag the item to its proper location to equip.