Unless there is a certain terminology for "backside" plugs, this is a plug (or as I know it: a wobbler. No idea which term is more commonly used around where you live).
I had to bust out my detective hat and pipe to find information on these ones, but I stumbled upon this: an article about this bait
They are(?)/were made by bomber, and nowadays you find them as Arbogast Mudbugs. (Note the two notches vs one notch in the bomber)
Now on to plugs as I understand you question being for plugs in general, not your bait specificly. There are some different types, some with shovel, some without.
The ones without shovel usually sink, and depend on you to perform, you twitch your rod and work the bait to make it "jump" through the water like an injured fish. With some skill you can walk it through the water impressively (you make make it do sharp 90 or even 180 degree turns). But I don't want to focus on these baits, lets focus on the baits with this "shovel".
The shovel can determine how deep your lure runs at certain reeling speeds. These lures typically float (or suspend in the water), and only start to dive once you start reeling them in. You can make it more attractive by adding some twitches again, sometimes you even have to. But usually it "wobbles" from side to side, which attracts fish.
To answer your questions specifically:
- This is a type of plug, you find some more information above
- You use them to catch predatory fish. Depending on the action you can just cast-and-reel these baits, adding some more action yourself. Depending on the baits action, you will use reel-speed to get it to your preferred depth, and then slow down and start working your bait. You reel slowly, you stop and let the lure rise to the top, then you start reeling again to make it dive. Or you just reel at a constant speed. Plugs have a diving depth at which they don't dive much deeper. You are constantly pulling it upwards, and the shovel pulls it downwards, at some point you will reach a balance.
- You will catch predatory fish with it. It it eats living fish, you catch it. I even had birds attack wobblers of mine.
On why this lure seems to perform so much better than other, modern lures: Chances are that it doesn't. You were successful with it and use it again, thus you remain successful with it. The most successful lures are usually ... wet. You use them, you catch fish with them. Since this lure seems to be more uncommon than most modern lures, it might acutally have an advantage as fish might be less timid towards it. All those shiny, rattling, loud lures in the water, and suddenly there is a lot of movement amongst fish, as you catch one of them, chances are that this stress makes fish avoid these new types of lures. On the other hand, they still catch fish, so who knows...
So who knows why your lure might be more successful. Fish don't know it yet? It looks like some type of familiar food to them? You were lucky? The lure just performs better than modern ones? Maybe it just has the perfect diving depth for your lake, or it dives at a speed that perfectly passes each water depth, aiding in finding fish. I can only speculate at this point.
Just replace your hooks once in a while ;)