Room Treatment

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.

Let me echo Polk432. My room is extensively treated with ASC bass traps and diffusion devices. However, after all that there were still two bass modes that the traps couldn't ameliorate. The PARC worked wonders. Not cheap, approx. $3500, but worth it.

I got lucky and found one on the bay for 500.00 9 of 10 condition, and the unit really works. Way better than spending lots on bass traps that don't do as good a job. I was thinking of having my listening room done professionally, but who knows the final outcome. Even if I made a big profit on the parc. I'd never be able to replace it for what I paid. It even has a bypass if you want extra bass for certain music.

Idleally it best to know what the problem is before trying to correct it. You could do find modes based on your dimensions, which shows four coincident modes I believe at 141hz. More accurately, and relatively inexpensively you could do room acoustic measurements with room eq wizard.
Low frequeny pressure is highest at walls and corners, so that is why there was "excess bass". Not a problem unless you listen to music there. A secondary issue to low frequency response is modal decay time, which sounds better if generally shorter and uniform.

I have had a a lot of benefit from placing speakers using the golden ratio. Another technique is to offset speaker and espcially listener placement by a few inches relative to room width.

Higher frequencies are easier and can use simple panels or diffusers at reflection points.