One of the big differences is the way that LR works. You (should) still start with a good solid file storage structure. But that doesn't necessarily matter to LR. You 'import' your images, at which time LR saves a preview and registers where the file is stored (as a database). From that point on, anything you do, in terms of editing, within Lightroom, is stored in the catalog and sidecar files. None of the edits/changes are applied to the image, thus leaving them untouched and thus undamaged. Some call this parametric editing, some call it non-destructive editing...whatever. So there really is no 'save' button...it's not the typical open, save (overwrite) type of workflow.
One of the benefits is that you're not damaging the photo during the editing process. You can go back, change anything, as often as you want. Sure, you can do this with layers and such in PS CS, but it's not functionally the same.
So when you're done editing, you 'export' and LR spits out copies of your images, with any specific settings you might want to apply (file size, resolution, color space etc.) You can still go back and change 'the original' and have it spit out something different. Again, you can do pretty much anything in PS CS, but Lightroom just makes it faster and easier IMO.
Yet another benefit is the speed at which you can go though your images...especially with an 'optimized' workflow. For example, the workflow I tech in my LR class, is to first go though and cull/weed whack the images, then go though and pick/rate/label them. Then go though and crop/straighten, then go though and deal with exposure (basic panel), then go though and deal with color, then go though and deal with details & effects. In other words, rather than taking one image at a time and going though your workflow, you take one or two aspects of the workflow and you run though all the images. It seems weird at first, but it helps to run though a lot of images in a more efficient way.