Attention is a critically important aspect of daily life. It helps us maintain concentration, incorporate information from our environment, and learn new things. Without attention, we wouldn't even be able to put our thoughts together.
It allows us to concentrate on one thing at a time while ignoring information that might distract us. There are lots of structures in the brain that are responsible for helping us sustain attention... my favorite being the locus coeruleus, because it sounds like a Roman conqueror sent to lead the way towards better attention!
You may have heard of the term multitasking, but this is actually not a real phenomenon. It's probably better referred to as divided attention because your brain cannot actually attend to more than one task simultaneously.
In people who don't have ADHD, our brains have systems in place to help us ignore incoming stimuli, so we can focus on one thing at a time. We are also better at being able to recognize when a boring task requires our attention, and, even though we may not want to, we can still muster up the energy to sustain attention long enough to get through it.
Now, take everything I just said, reverse it, and BOOM, you've got ADHD. In a person with ADHD, their input control systems are out of whack. Their brain lacks the control needed to ignore their impulses and incoming sensory information from the surrounding environment.
They can't tune out how their body feels so they move around, and have difficulty sitting still in their seats. They have trouble paying attention and staying on task because the clock is ticking, there's a noise in the hallway, one of their friends is laughing, the sun is too hot on their skin, they're thirsty etc.
If the task is boring... it's pretty much a non-starter. They need multiple directions to stay on task and constant monitoring to follow through. They may come across as lazy, or distracted, which can drastically effect how they view themselves because they may want to pay attention, but their brain just isn't allowing them to.
From a neurobiological basis, ADHD is too much slow wave activity (theta) and not enough fast wave activity (beta). Neurofeedback for ADHD involves rewarding the brain when it is producing more beta waves and taking away the reward when it it is producing more theta waves. Neurofeedback helps the brain learn how to close down those impulse systems. It teaches the neurons responsible for being too open to all of the feedback they are getting from their bodies and the environment, to basically shut up.
By doing this, the person is finally able to sustain attention and filter out the unnecessary junk that tries to get in the way, which can lead to better grades, better work performance, better ability to stay on task, improved mood... you get the idea.