I suppose it's like a tradition to say this.
It could go like, "I guard your back while you guard mine"
Not necessarily fight related.
A mutual relationship formed
In Japan this is a very common thing to say in a wide varity of situations. Even when you're meeting someone for the first time it's not unusual. Keep an ear out for the phrase "yoroshiku onegaishimasu" and its variants while watching anime and you will hear it all the time.