Basically, the timing is just how a human being does exhausting work, isn't it? The exact minutes aside, you work for a bit, then you need a break (5 minutes is nothing, really). After a while, you need a bigger break. It's how I do it, without thinking (and admittedly, whenever I break that kind of cycle too drastically, I get unproductive).

I feel like a lot of these "life hack" kinda things are essentially just little pieces of entertainment/motivation you need to muster the initial energy needed to break a bad habit. Pomodoro sounds fun, it means tomato. It might let you fiddle with an app. You can track your progress and have fun charts to compare with potentially exciting results. And you have a story to tell people when they ask about your work.

The actual benefit of partitioning your day into exact 25 minute intervals is probably negligible, but while you're dealing with all this, you're actively working on being more productive and that alone has its benefits. It's probably a chicken-or-the-egg problem or even a plain old placebo effect, but it seems to work. Especially engineering types (as most people on hackernews) tend to have a problem accepting how convoluted psychology is, but sometimes just the decision to try to fix something fixes it.