What is this flat metal sieve that came with my pressure cooker for?

The sieve-like item is a steamer insert, used to cook things that do not cook well if submerged in the comparatively large amount of water a pressure cooker needs to operate. The wire is a stand for this insert, to raise it above the waterline.

Unless you bought it used: Pressure cooker makers tend to give free books away with their pots, often a classic about a spanish guy called Manual. Good reading while watching a pressure cooker.

If you just put the metal dish into the pressure cooker it has three dimples pointing down... so anything standing on top of it is not in contact with the physical bottom of the pan. The idea being that if you put some flat-bottom or concave bottom jars in they don't end up directly sitting on the pan's bottom. that could lead to hot spots under the jars... if you are bottling (canning in glass) stuff in the pressure cooker that could lead to burned contents or a cracked jar.

It's often called a trivet.

My mother's one didn't come with a wire stand... it just relied on the dimples to keep it off the bottom.

Use the trivet and sieve method to cook eggs. Separation from the cooker bottom keeps them from bouncing in the boiling water and sometimes breaking open.