Room Treatment

That's a good sized room; have you tried clapping your hands in the center of the room to hear how "live" it sounds? Does the bass sound tight or is it boomy? You may find that you need some absorption or diffusion panels.

It's good that you've got the speakers away from the walls, but 2 vertical absorption panels behind the spkrs and 2 on side walls would benefit, just as Ghosthouse has suggested.

My room is L-shaped and I'm trying to figure out if I will benefit from bass traps. What are bass traps designed to accomplish?

Simply put, bass traps absorb low frequency sound waves in order to achieve a flat frequency response so the music sounds balanced when it arrives at your listening area (most often using an SPL meter).
That's why I said to listen for a booming bass sound or if the bass in your room sounds tight, (tight is good). A bass trap can absorb these frequencies if too much bass, or bass does not sound well defined.

The sound panels on the walls as suggested will absorb or diffuse standing waves that bounce around the room. Think in terms of a concert hall that has been treated to have an even, well distributed sound.

The simple hand clap test will let you hear if there is any echo in the room. If so, add panels to the walls and many times the ceiling.