In the state of nature, if someone does you wrong, it’s up to you and your mates to deal with it. This often means violence.
For most of English history there was no police force. Republican Rome had no police. There was law, but it was often privately enforced and often families and friends would take vengeance for wrongs. This led to rather a lot of violence and death, as well as feuds, where violence would continue long beyond the original offense.
Private justice; private vengeance thus comes with huge downsides, so in many societies we give up our right to use violence to right wrongs. We give that right to government in some form, and we reap the benefits of safety and that, in principle, stronger groups can’t bully those who are too weak to obtain their own justice.