Chanting Different Songs from the Hebrew Bible

I was very surprised that, even though it is considered chanting, it still is very musically based and has many characteristics of singing a normal song. Those chanting often still added flourishes and did not chant in the same tone throughout the song. Also, I saw in the example from New York City that at one part of the chant everyone covered their eyes. Why did they do this? Was it part of that specific song, or is this something they would do for any of the songs they chant?