For those religious Jews I have a question about praying at the Western Wall in Jerusalem?

I'm a Christian & going to Jerusalem in October & will visit "one of the holiest places in Israel" & while watching a Geographic show about Jerusalem, it showed people praying there. It said Christians can also pray there but their heads should be covered & we could leave our prayer notes there, as Jews do. I'm wondering why some Jews praying there, keep a rhythmic bowing action going while they pray? I'd like to know where the tradition comes from. Also, why do some Jews strap on a small, black strap on their foreheads with a 2 " cylinder-like projection on it? Since I will be there soon, I'd like to know why they do this & why others don't? I'd like to know where the tradition comes from. I thank everyone for their information. It is appreciated.