Bird dog exercise helps reduce lower back pain by strengthen your core, the abdominals and lumbar spine muscles. In addition to strengthening your core muscles, this exercise teaches you hip mobility with back stability. This means you are learning to engage these stabilizer (core) muscles, and making them do the work to take pressure off of your spine during every day movement and while exercising.
Bird dog also works the glutes. Remember to engage the glute each time you extend your hip back and straighten your leg parallel to the ground.