To the extent that the Civil War still impacts us today, it is because of the fact that the war helped to make the North and the South seem distinct from one another. There continue to be major political and cultural differences between the South and the rest of the country to this day.
In part, of course, these differences were caused by the slave system rather than by the war. However, the war caused there to be some amount of lingering resentment between the two sides and caused the differences to be emphasized over the years. For example, it is partly because of the Civil War that there are still conflicts over things like the use of the Confederate flag.
The Civil War helped to make and keep the South different from the rest of the country. These differences still show up today in our politics and in our culture. In this way, the Civil War does still have an impact on our lives.