Grand Theft Auto III's GameplayGrand Theft Auto III set a new president when it came to open-world, sandbox style gameplay. The player is quite literally allowed to do whatever they want. Stick to the story and complete missions. Go out and track down the 100 hidden packages. Find the various special vehicles which contain side-missions like checkpoint grabbing, or RC vehicles rigged with bombs.
And if that's all too boring, you can just drive around the large city stealing whatever cars you want, killing whoever you want, fighting with cops or banging prostitutes. Why not grab a tank from the Army and go around smashing the shit out of everything?
I think this makes it fairly clear why Grand Theft Auto III was ground breaking at the time of it's release in 2001.