Before answering this question, let's look at what happened before.
When Napoleon invaded Russia, he indented to take Moscow which he presumed would have resulted in the surrender of the Tsar.
But for Tsar Alexander, Napoleon had become the Antichrist, and his divine mission to defeat him.
The sac of Moscow didn't change the mind of Alexander, resulting into the catastrophic retreat of the French and allies.
The Tsar in his belief persuaded and pushed everyone into a anti-French coalition which ended into the campaign of 1814 and the fall of Paris.
With the common enemy gone, the negotiations afterwards turned into a hostile atmosphere.
Louis XVIII wasn't very popular and a major part of the population began to support a return of Napoleon.
Being married to the daughter of the Austrian Emperor, and Austria at first being reluctant to join the Russian anti-Bonaparte coalition in 1812, Napoleon hoped that with the negotiations turning sour he could form an alliance, and return to power. He made his move and returned to France.
But with their common enemy again on the field, the allies let go their quarrels and restored their coalition. Tsar Alexander had no intention to drop his Divine goal to fight the anti-Christ.Also Napoleons wasn't the best negotiator, almost all his victories ended with dictations.
He turned to the one thing he was good at. waging war.
However, he must have know his situation was hopeless.
Would Great-Britain be knocked out of the war with one big defeat? Don't think so, after 10 year of permanent war giving in after oone setback? Would the Dutch prefer a new French domination over Independence? No chance.
Did Prussia asked for peace after the defeat at Ligny? Of course not, they did receive several heavy blows in the 1814 campaign but had continued the war.
And above all, in the East, there was a massive force building up. 500.000 Russian, Austrians and other allies were gathering to start a new 1814 campaign.
As numbers do count, chances for Napoleon were zero.
let's also not forget the support he received from his coutnymen was also limited: the French were war-weary. Even berthier didn't return to service. He had to leave Davout, his best commander in Paris to cover his back, and kept turncoat Ney close.
So why is battle of Waterloo important? It certainly was the last battle of Napoleon, ending an era. That is the big importance of the battle.
Did it change history? No, it shortened the last convulsion of Bonaparte power. It can be compared to the battle of the Bulge in WWII. A desperate move with overoptimistic goals, but doomed to fail.
Of course, it also is the biggest battle the British fought against the french, and the only confrontation of Napoleon himself against a British dominated army.
In this Anlgo Saxon world, the battle has received his mythical status. Made the Iron Duke the man who defeated Napoleon. If one looks at the whole picture, one knows Tsar Alexander was Napoleons Nemesis.