When this muscle is tight, it can pull the lower back forward increasing the arch in the low back. This extra arch is one of the causes of low back pain.
The best relief for the psoas is a massage, however there are not many massage therapists who can do a good job. Stretching the psoas is another way to help relieve the problem. Here are two stretches for the psoas that might help you and your back.
The best stretch I know of for the psoas requires a little help. They don't need to be skilled, they just need to be able to move slowly and respond to your instructions. Start by lying down on a massage table or high bed. You need some height, so that the leg you are working can be hanging down off the side. Lower is okay, as long as you can bend your knee so that your knee can be drawn down.
Let your leg drop completely, relax it. If need be, the top of the foot can be resting on the floor. Have the other leg extended fully so it is flat. Your helper then takes your foot in one hand drawing it up and slightly and towards your head while the other hand gently and very slowly draws the knee down.