Lightroom is a photo library management and photo development program. It is used either instead of, or in conjunction with Adobe Photoshop.
Why would I choose to learn Lightroom instead of Photoshop?
Once you have taken more than a hundred or so photos, you will need some way to organise them. Lightroom is the solution. If you want to adjust the photos' brightness and contrast, along with other more advanced adjustments, Lightroom will do that quickly, non-destructively and using the minimum amount of hard drive space possible (unlike Photoshop).
Why bother with Photoshop then?
Because more advanced and more detailed editing is still possible with Photoshop. However, for many photographers, this is not necessary, so Lightroom may be all they need.