The original format for competitive games in that style (think Tetris) was basically just a race to score more points, the 'race' part sometimes being optional. The original Puyo Puyo made it so that when you clear blocks, you send garbage blocks to your opponent's side to fill their stack. However, since you only needed a 6-chain to do it, every Puyo Puyo match was a race to build a 6-chain first. Other games that adopted the system had the same or a similar issue, and then PP2 was released with a rule that if you had garbage waiting to drop on you, but then you started clearing blocks before it fell, you would clear the amount of garbage you would've sent from your own stack first, and only then send any garbage that you score on top of that.
Rather than a pure chain race, offsetting makes games a lot more strategic: do you annoy your opponent with small chains or try to go for a big one, and if they start clearing, (when) do you start your offset? If they've got a one-hit-KO 6-chain ready, but you have one too, do you try to raise it to 7 so that you'll send your own counter-blow back, or pull the trigger now and force the other guy to respond? That was PP2's competitive edge in the market, and it was big enough that every block-dropping game since it came out has that rule.
30 years later, Puyo Puyo 2 is still the single biggest influence on the entire genre, and that by itself would be enough to make it important. But it also gets everything else so right that even its own sequels really only change the graphics (with any changes that do happen usually getting panned so much they don't get used again), and that's why it's the greatest of all time.