What exactly did the iPhone do better?

Perfected multi-touch touchscreen

Before that we had touchscreen but they sucked.

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    2002: FingerWorks makes advances in multi-touch technology
    2005: Apple acquires FingerWorks and its patents
    2007: iPhone launches

I really don't think multitouch is what made or broke the original iPhone.

That's a subjective question, so I'll give a subjective answer. The browser, for better or worse, was a lot less dumbed down for mobile than competitors, the stylus-less touch interface reduced UI friction and the odds that you'd lose a critical (if inexpensive) component, and the slew of contemporary iPod users could easily migrate their libraries over.