This question is more suited to a book-length answer or more. To generalize as broadly as possible, I would point to two major impacts that the criminal justice system has had on the black community.
First, the criminal justice system has, especially recently, jailed much of the black male population. As the "crime" link below tells us,
Approximately 30 percent of African American males aged twenty to twenty-nine are under the control or supervision of the criminal justice system—four times as many as Caucasian men in the same age group.
This ends up having huge impacts on the community as these men lose much of their ability to ever find a good job after they get out. This contributes to lower marriage rates as women decline to marry men with low prospects. It also, of course, tends to increase poverty and crime.
Second, the sheer amount of negative contact with the police leads many in the black community to distrust the police completely. This negative contact ranges from the relatively trivial (people pulled over for "driving while black") to the very serious (black people shot by the police for what turned out to be no good reason). This has led to a great deal of hatred of the police.
There are many other ways in which the criminal justice system has impacted the black community, but these are the most important.