After you get a paper cut, it's important that your body closes the cut (the wound) so you avoid getting an infection. There are three stages of wound healing to repair the cut. The stages are kind of like what you might go through if you tried to build a house.
First, the site has to be prepped and planning begins. Special cells called neutrophils are called in to help. They attract other immune cells and help trap invaders. During this inflammatory phase, your body stops blood loss by clotting the blood and reducing blood flow. Lots of "supervisors" like proteins, blood cells, and antibodies are sent to the site. Macrophages are a critical part of this wound healing team. They come to clean up the site before the building can start. They eat the dead skin cells and other waste around the area.
Once the wound is free of germs, the waste is cleaned up, and the skin growth started, the macrophages and neutrophils start to leave. It's important they leave because having inflammation for long periods of time can cause serious problems.