Lightroom basically is a raw converter—the same as Camera Raw—wrapped up in a digital asset management program, i. e. software to import, store, sort, retrieve, and export digital media (that is, mostly photos).
The basic difference between editing in Photoshop and editing in Lightroom is this: Photoshop can do all kinds of local adjustments; Lightroom is limited to global adjustments. Global adjustments are those which affect the whole image—i. e. things like increasing or decreasing colour temperature, colour casts, brightness, contrast, or sharpness. Local adjustments are things that are done to parts of the image only and tyically involve selections, masks, and layers. However these days, the borderline between local and global adjustments has become somewhat blurred, as Lightroom (and Camera Raw) also can do some limited local editing. Still, for full-strength local editing, you do need Photoshop (or another post-processing program). For the vast majority of images, however, Lightroom's editing capabilities are more than adequate.
