To do justice to Lightroom would take a proper full review so this is incredibly potted, but here I go.
Adobe PhotoShop is a general purpose raster based image editor, and it's very, no make that extremely good at what it does. However for the professional photographer there are repeat processes that need doing over and over, sometimes for vast numbers of images. Lightroom will completely automate some of these tasks, and make others much easier than straight PhotoShop can.