Just in case your first exposure was from a different source, people started saying "black lives matter" because of the instances where people acted callously or apathetic towards the lives of black people, and the centuries of history in the Americas that are congruent with and reinforce that reality continuing now.
It has since been assigned to a faction and movement that has very little to do with the point of why people are saying it.
Hope that helps someone! There are a lot of people that think this came out of the blue and interpret the chants as an impending pogrom putting some people's lives above others, but that is a distortion that is furthest from the truth.