Historically, Jim Crow laws served to enforce racial segregation and deny the vote to African Americans. This was achieved through such measures as legally segregated schools and public facilities, poll taxes, and literacy tests at the polls. This system relegated African Americans to a status of second-class citizens.
Just because official Jim Crow laws were done away with as the result of various civil rights acts and court decisions does not mean that they do not still exist in a less official form today. To best answer your question, let's look at some examples of what has been called the New Jim Crow.
For starters, the criminal justice system has long disproportionately targeted African American men, particularly as part of the war on drugs. By saddling so many people of one race with permanent criminal records, it makes it significantly more difficult for them to find gainful employment, education, and housing. Furthermore, a number of states practice criminal disenfranchisement, effectively preventing a significant part of the minority population from voting.
When looking for new and old Jim Crow practices to compare, you can consider which ones were and are used to prevent people from voting, living in certain areas, and receiving public services. The difference here is that historically Jim Crow was based purely on racial characteristics. Today, it is justified as being an offshoot of the criminal justice system. However, it is important to note that the mass criminalization of a particular racial demographic has effectively recreated much of the former system.
To answer the last part of the question, consider how Jim Crow is both antithetical to public safety as well as American notions of justice and democracy. By relegating a large portion of the population to second-class status, many minorities are denied fair employment and housing opportunities. Furthermore, by denying many minorities the vote, congressional districts are skewed away from truly representing their constituencies, and many people are left without a democratic voice.