Things often involve more than their names might imply. Case in point: Black Lives Matter.
A lot of people react to the phrase "Black Lives Matter" without taking time to understand what's behind it. It was prompted by a series of incidents in which government authorities in a number of places in the U.S. seemed to treat black lives as mattering less than others. (This includes not just police killings of black persons but a tendency to treat more seriously crimes committed against white persons.) Members of Black Lives Matter have proposed a number of practical steps to make things better, such as improved police training.
As with anything else, there are legitimate grounds for disagreement. Some cases that have been cited by BLM advocate may not actually reflect racial bias or police misconduct (though plenty of others pretty clearly do). There are other cases involving white victims of police misconduct that would probably be held up as examples of racism were the victim black. (This one, for example.) That is, bad behavior on the part of the police can have other causes besides racial prejudice. It's worth noting that a lot of Black Lives Matter ideas (including, as mentioned, better police training) would probably help no matter what the underlying cause and regardless of the race of anyone involved.
But a lot of objections to BLM simply miss the point. Yes, all lives matter. Yes, the vast majority of black homicide victims are killed by people of the same race. (That's also true of white homicide victims, by the way.) Yes, homicide rates are higher for black people than for white people. Black Lives Matter doesn't say otherwise; it's just addressing something else that's a legitimate topic of concern. Maybe it would have been clearer if the BLM movement had adopted the slogan "Black Lives Matter Too."
Below vlogger Vi Hart summarizes the history of the Black Lives Matter movement. I have quibbles with some of what she says, but in the main I think it's a useful and interesting video essay.
(Updated 2017 August 16 in my usual attempt to express myself better.)