The core is at the center of the body, and I think of it as the body's headquarters. Everything else including hips, pelvis, lower back, work in conjunction with the core. If the core is strong, then everything attached to it works from a solid foundation. I once had a Navy Physical Therapist tell me that I would have less injuries in my extremities if I increased my core strength. So that is when I got serious about strengthening my middle.
Core strength can significantly help with lower back issues, posture, and balance. One workout that I really like for building core strength is the PiYo workout. This workout uses all of your own body weight to build upper body, lower body, and core strength. The flexibility training in this workout is game changing for runners because it can actually lengthen a runner's stride. It strengthens and stretches hip flexors, quads, hamstrings, glutes, and lower back. There are a lot of planks, side planks, and pushups which is great for core strength. (Click HERE to get the PiYo workout.)
As far as equipment for core work, I am a huge fan of the Bosu ball, medicine ball, or simply using your own body weight. Ironman University has a complete data base for exercises for each discipline, so I put together a list of all of the core strengthening moves and created this little video specifically for RUNNERS! You can add your own moves to this and have some fun with it! If you want me to create a custom core strengthening program for you, then message me HERE.