Lightroom was developed because many working photographers felt like Photoshop had a lot of "stuff" they didn't need and then a lot of "stuff" they used only occasionally, and that all that "stuff" had the effect of cluttering their workspace and, when it came to their normal "workflow" had a way of making things more complicated and less efficient than they needed it to be.
A lot of shooters had adopted the Raw format to get the most out of their photos without resorting to the type of manipulations that Photoshop specializes in, and so a team of Adobe developers, including the engineers of Adobe Camera Raw, put together a "photographer's workflow managing application" built around the same Raw processor as was found in Photoshop CSx. It combined the common file management and photo organizing tasks with output tasks like printing and exporting converted Raw files all together with the Raw processing into one integrated interface, and made things like batch processing a matter of simple integrated steps so that a photog could do much if not all that was needed without having to hop around multiple interfaces and dialogs, the way we did things in Photoshop.
That being said, a Photoshop user doesn't "need" Lightroom, because you can do virtually all Lightroom does within CSx. It is more a matter of workflow efficiency. To me, LR is a great workflow tool, it does all I need for almost all of my photos, and for the few that require Photoshop touches, it has easy ways of transferring files to PS and some (like using PS droplets) that enable batch processing in PS as well.
Ironically, LR has been so successful (and Aperture on the Apple side that has a similar "model") that many photogs don't ask "do I really need Lightroom if I have Photoshop?" but rather "do I really need Photoshop if I have Lightroom?", and many have happily adopted Photoshop Elements as a lighter, simpler and way less expensive way of handling the occasional image manipulations while happily doing the volume of photo processing in Lightroom.
It should also be said that the years since Lightroom was first released have seen some dramatic enhancements to Raw processing that have even more made the Raw-centered workflow a rich and compelling experience -- in fact, just this week lens distortion correction was added to ACR (6.1) and will be seen in the upcoming LR3 -- I don't know about others, but seeing this added made me feel like "Kerchunk! Another very cool piece falls into place" and gave me a bit of a chill of pleasure
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I'll also add that advances in Raw processing can also be seen in other non-Adobe products. Aperture is, like I said, built on the same "one interface does all" model and has most of the tools that Lightroom has (but lags behind in the newest innovations like the lens correction I mentioned) and even the Canon DPP has been increasing its capabilities -- not aproaching those of Lightroom, but still able to deliver great results and many photogs have taken up DPP rather than Lightroom because of that, but for the integrated interface as well as the advanced toolset, Lightroom to me still hits the spot.