Think of it in terms of volume. Where PS is good at doing alot of detailed edits on a single photo, or a small batch of photos at a time, LR is built for large volume automation, indexing, sorting. It has a limited feature set identical to PS, basicly most critical image processing features in PS are also available via LR.
In addition, with LR you can apply a preset on 1000 photos, create slideshows, create books, make backups, catalogues, filters, etc. Also, everything done in LR is non-destructive, will not affect actual photo source files, but instead edits are saved as a separate database and no actual saving is done on the photo files.
You may get around fine with just using PS if you're not shooting alot of images. LR is more useful for large amounts of photos, for instance studio work where the same shot is taken dozens of times in different variations or in burst mode.