I always thought it was the gems she wore and the one in the middle of her weapon that produced the shield, but Sivir's lore doesn't really tell much about her. Except that she's filthy rich.

It's just as you see it - the gems that people wear in their armor are usually meant to hold Mana. Sivir deflects spells with her crossblade (the icon for the spell also displays it), and absorbs a portion of the spell's power as bonus Mana if she succeeds. It's sort of like Fiora's parry - it's very hard to make this animation due to net delay, and so it just looks like a magic-y shield. But in reality, Fiora actually deflects the enemy's attack, and Sivir blocks spells with her crossblade.