Pomodoro is just the Italian word for tomato. That's the entire etymology. The most widely adopted focus method in the world is named after a piece of kitchen equipment shaped like a vegetable that is technically a fruit.
Late 1980s, Francesco Cirillo is a university student in Rome and he is drowning. Not in a dramatic way — in the extremely common way, where you sit down to study and two hours later you have read the same page several times and accomplished nothing measurable and feel worse than when you started.
So he made himself a bet: could he actually study, properly, for ten minutes. He grabbed the wind-up timer off the kitchen counter, the tomato one, set it, and tried.
No productivity philosophy anywhere in it. A guy trying to prove he could concentrate for ten minutes.
What he'd stumbled into
The interval settled at twenty-five minutes with short breaks between, and the method spread far enough that it now has books, apps, and a small industry of people arguing about the correct break length.
But the mechanism people usually credit — twenty-five minutes is the optimal attention span — isn't really it, and it isn't especially well supported. What the timer actually does is smaller and better.
It makes the work finite before you start.
An open-ended study session has no shape. It stretches ahead of you as until I'm done or until I can't anymore, both of which are terrible things to walk toward, and both of which your brain will negotiate against immediately. Twenty-five minutes is something you can hold. You can see the far end of it from here. Starting is a completely different proposition when you already know when it stops.
The ticking helps too, by all accounts, including Cirillo's. Time stops being an abstraction and becomes a noise in the room.
Where it stops working
Pomodoro handles the starting problem well and the planning problem not at all.
It'll get you into focused work. It won't tell you whether the thing you're focusing on is the thing that should have your next twenty-five minutes, and it has no opinion about whether the eleven other things on your list fit in what's left of the day. Run four flawless pomodoros on the wrong task and you have executed beautifully in the wrong direction.
It's a tool for the last mile. Most people's actual failure happens well before the last mile, at the point where you're staring at a list trying to work out which item deserves you.
Both halves
IHC does the part the tomato doesn't. It sizes the day, works out what fits, and puts the right thing on top — so by the time you're setting a timer, the choice has already been made and made well.
Then "Plan my… free moment" handles the rest of it: say you've got twenty minutes and the plan fills them from your list, highest priority first, counting against the same budget as everything else — so a block of work isn't a thing that happens outside your plan. It's a chunk of the plan getting done.
Cirillo's real insight was that a finite piece of work is enormously easier to begin than an infinite one. He applied it to a study session. We applied it to the whole day, which needed it more — your Tuesday has edges, and everything gets easier once the list knows where they are.
Sources: Francesco Cirillo, "The Pomodoro Technique"; cirillocompany.de.