To bring it into a broader sense, look up a map of Tamriel. The Thalmor are the bourgeois class of the Dominion, which is the combination of Summerset Isle and Valenwood.
Not quite. First, don't bring newspeak into this discussion. The Thalmor are Elven supremacists that rose to power in the wake of the Oblivion Crisis, exploiting the fall of the Crystal Tower and the myth they carefully nurtured that they, the Thalmor, saved Summerset Isle from certain destruction. After purging any and all opposition, they managed to orchestrate the secession of Valenwood from the Empire and bring Bosmer into the fold.
Then, the Aldmeri Dominion was refounded.
The Great War they speak of was when the Dominion attempted to, and with mild success, defeat the Empire. After the war the Empire seceded Hammerfell, which is home to the Redguards, and they didn't like that too much. An epic war took place between the, now independent, Hammerfell and the Dominion. Hammefell managed to stave off the elves and retained its independence.
The Great War was a major military conflict that took place after Emperor Titus Mede did not heed the Thalmor ultimatum (which was really insulting to the Empire and included outlawing the worship of Thalmor). The War was bloody, pretty much broke the Empire's back (when the Emperor retook Cyrodil with Nord legions, the Empire was in absolutely no shape to continue the war, with much of its legions at half strength or less). It wasn't a mild success for the Altmer, it was a full victory, considering that the White-Gold Concordat was exactly the same document as the ultimatum.
And Hammerfell was cut off from the Empire because they refused to give up and continued the War. It still rages on (after all, the Alik'r make explicit mention of a resistance movement in Hammerfell) between the Redguards and the Thalmor, who occupy the southern parts of the province. It's far from over.