As the other answer suggests, the idea of a "finisher" is just to maximize the output of your workout by pushing the muscles to more complete failure. Remember that building muscle is about making your brain recognise that your strength isn't sufficient to cope with the demand you are placing on it, therefore it triggers muscle growth so that next time you place those same demands, your body copes better.
Imagine you do a routine of 3x10 reps of bench press. You increase the weight each set but still manage to complete all 10 reps of each set. You can either move onto another exercise (even a different muscle group) and still get good results, but what if you could do another 6 reps providing you dropped the weight? The theory is that you are reinforcing to your brain the idea that it needs to make your muscles adapt because you are adding some extra stress, therefore the results should be slightly improved. A "ladder" is the same idea but repeated again and again with reduced weight.
There are many ways to train, and despite what you read online, no absolutely "right" way to work out - everyone is different, and what suits some people may not suit others. I certainly don't do "finishers" on every workout, especially if I'm feeling a bit tired. Remember the risk is you might overtrain, possibly causing injury or at least reducing results if you aren't getting sufficient recovery and nutrient intake.
My recommendation would be to give them a try on half of your weekly workouts and see how you feel. If you can stay injury free and they do give you a feeling of a more satisfying/thorough workout then keep doing them. Just remember there are limits to how quickly you can gain muscle, and getting 100% from each workout isn't a realistic possibility, but getting 85% instead of 70% obviously helps and there are lots of ways to achieve that. "Finishers" are just one such way.