The key aspect of the brain that is wonky in a person with ADHD is what’s called the “central executive”. This is the part of the brain that’s in charge of filtering the thousands of inputs we’re constantly subject to. Things we can hear / see / feel etc. and thoughts we’re processing*
In a “normal” brain, 99% of this is filtered out completely and only gets to your actual thought process when it has some level of pertinence. In an ADHD brain, these things tend to come through jumbled up and all shouting for attention at random moments because the central executive is weak. It’s a bit like the secretary outside the boss’s office taking phone calls and visitors and telling most of them to wait (or go away) while selecting one at a time to actually talk to him.
Stimulants stimulate the central executive, meaning you’re able to spend your brain power on the actually important stuff (well, the executive isn’t prescient, but it does a pretty good job when it’s doing its job!).
As a side effect, the stimulants also stimulate various other stuff (heart rate, kidney function, other bits of the brain…) but the bit that’s most noticeable in a brain with a broken executive is that the executive is suddenly less broken 😛
* Right now I can count 5 distinct noises and see dozens of things in a dark and “silent” room, as well as feel half a dozen points of contact between my body and the furniture, the residue of the last thing I ate in my teeth, the rims of my glasses, the tension in my back from the weird way I’m sitting, the callouses on my fingertips, the years old break in my hand that’s aching today, the sore spot on my lip… I’m also thinking about what I’m typing, the song that was just on the TV programme I watched, the fact that I haven’t had a lucid dream in a while, whether this post is too long for an ADHDer to bother reading and so on ad nauseam.