I don't understand what the different software programs do, or why I would need both of them, but I can dig into that myself.
I'm assuming you're talking primarily about Lightroom vs. Photoshop. I'll see if I can help explain it a little, but ultimately you may just want to go to the Adobe homepage and download the free trial versions of each to see for yourself.
Lightroom: This was primarily designed as a tool for organizing your photos with some basic editing functionality. The methodology it uses for organization is a bit different than the normal folder structure most of us are used to in Windows, so it takes a little getting used to, but it's a very good architecture. Over the years, Lightroom has become a rather powerful photo editor in its own right. Probably the biggest difference in that aspect between Lightroom and Photoshop is that Lightroom is what's called a "non-destructive" editor. In other words, it doesn't make any changes to the actual file. It uses what's referred to as a "side-car" file that's basically a list of the adjustments you've made which are layered on top of the original file when you view it. You can then always export the file along with its adjustments as a jpeg, tiff, etc., so the original file is intact, but you can use the exported file in a web page, to send off to the printers, etc.
Photoshop: There are two versions. If you just here "Photoshop", it's generally referring to the "full version" of Photoshop, which is part of the Photoshop Creative Suite (CS). Then, there's the scaled down version which is Photoshop Elements. They both work the same way, but Elements lacks some of the functionality that Photoshop has (though it's still very powerful). Photoshop and Photoshop Elements are what's often called "pixel editors". In other words, you can change the actual pixels in the image, physically changing the contents of the image file. Like Lightroom, you can do all of your basic editing (brightness, contrast, color balance, etc.), but you can also do things like remove an unwanted object from the photo, blend multiple photos, stich photos into a Panorama, etc. It also has a lot of application in graphic editing. . .if you want to create a picture of your wife as a mermaid emerging from a waterfall, you're going to need Photoshop.
As I believe someone mentioned, the two programs were designed to be used in conjunction, but can also be used very effectively separately. I used Elements and then Photoshop alone for years, and just recently started using Lightroom. It took a little getting used to, but I eventually found the workflow in Lightroom to be much easier for basic photo editing. For example, I have profiles for candid photos, sports, landscapes, B&W, etc. that I can apply literally at the click of a button, and my photo editing is 90% done in many instances. Then, it's very easy to give the photo a title, description, key words, add it to a collection, etc. so it's very easy to find it amongst my 10s of thousands of photos in the future. On the other hand, if I want to do some serious selective editing, remove an offending tree branch or blend exposures from two different photos, it's time to go into Photoshop.