The Empire is a mainstay of the Elder Scrolls series going all the way back to the beginning, and just like in Oblivion and Morrowind they are an integral part of the events of Skyrim. The Empire was mostly a force for good in the third and fourth Elder Scrolls games, but Skyrim's version of the Empire is a bit more complicated thanks to the Oblivion Crisis and the Great War.
The Empire is one side in Skyrim's Civil War questline, who aim to quell the Stormcloak rebellion and maintain Skyrim as Imperial territory. The Stormcloaks have some understandable motivations, but at the end of the day, the Empire has more justifiable reasons to keep it as an Imperial Territory than the rebels have for destabilizing and threatening the safety of the entire region.
The Empire Stands A Better Chance Against The Aldmeri Dominion
When it comes down to it, the main reason that the Empire needs to win the Civil War is the threat of the Aldmeri Dominion. As of the signing of the White-Gold Concordat, the first Great War ended, leaving both the Dominion and the Empire to recoup and recover for the end of the ceasefire. The Stormcloaks rose up during this interim.
The Stormcloaks know Skyrim like the back of their hand, but the Empire is better able to defend Skyrim from the Aldmeri Dominion than Ulfric's followers. Under the Empire, Skyrim is relatively united under the High King and the Emperor. If the Stormcloaks win, Skyrim becomes completely destabilized and the Dominion will face little unified danger when trying to conquer the frozen north. If the Empire wins, the people of Skyrim will be part of a much larger, much stronger united front against the Elven invaders.
Ulfric Betrayed Skyrim's Traditions After He Killed High King Torygg
For centuries the High King of Skyrim was either chosen by birthright or, in the event of no heir to the throne, through a moot of the nine Holds of Skyrim. This moot saw the Jarls elect a new High King, typically related to the deceased High King or one of the Jarls themselves. As part of ancient Nordic tradition the High King can be challenged for the throne, something Ulfric Stormcloak took advantage of. There are two problems with Ulfric's challenge, one during the duel, and one after.
Nordic Tradition states that the High King can be challenged, but the fact that Torygg stood no chance against the Thu'um makes Ulfric closer to a murderer than the victor of a duel. After Torygg was killed Ulfric called for a new moot to elect a High King (as tradition states) but he then goes around Skyrim replacing Jarls who won't join him with loyalists, essentially forcing the moot to swing in his favor. Ulfric and his Stormcloaks kill all who stand in his way, including native Nords and true sons and daughters of Skyrim who simply refused to join him – not very traditional, Ulfric.
The White-Gold Concordat Is Ultimately A Temporary Agreement
The White-Gold Concordat was signed as a sort of armistice to end the Great War between the Empire and the Aldmeri Dominion. While the terms of the agreement are harsh, considering that most of it reiterates the Dominion's goals for the War in the first place, it's not a permanent agreement like the Stormcloaks like to think.
When the Aldmeri Dominion or the Empire are ready to start swinging at each other again the terms of the White-Gold Concordat will cease. Banning Talos worship amongst men is just not practical, there will always be worshippers in the shadows. No matter who wins the Civil War Talos worship will eventually be reinstated. It will take a longer time if the Empire wins, sure, but it's better to avoid Talos worship temporarily if it brings peace. Stormcloaks might bring Talos worship back sooner, but likely at the cost of losing Skyrim to the Dominion altogether.
If You Play An Elf, You'll Get Kicked Out Of Skyrim If Stormcloaks Win...
The Stormcloaks are fiercely anti-elven. Windhelm, the capital of the Stormcloaks, only allows Dunmer refugees because of the sheer level of devastation that Morrowind suffered – and even then, they're relegated to run-down slums and live segregated from the city. If Stormcloaks win, they will likely end up kicking all Mer out of Skyrim, whether they belong to the Aldmeri Dominion or not.
The Empire, on the other hand, is much more racially diverse and accepting thanks to its multi-national cultural roots. The Imperial race of man makes up a lot of the Empire, sure, but its wide reach brings in races from Elsweyr to High Rock and everywhere in between. The Stormcloaks only begrudgingly help other races, and only in times of need, but the Empire shows no particular preference. Just swear loyalty to the Emperor and you're in, no matter where you hail (although Altmer might have a hard time in the times of Skyrim).
...Even Though Skyrim Didn't Originally Belong To The Nords
The Stormcloaks believe firmly that Skyrim is the homeplace of the Nords, that they were breathed onto Nirn by Kyne at the Throat of the World from where they migrated around for Eons before finally returning back. The truth, or as close as official lore will get to it, is much murkier. The Falmer, for instance, were once a race of Elves that called the area now known as Skyrim home in the Merethic Era.
When the Nords invaded, they nearly completely wiped out this advanced civilization, forcing them to go underground, become slaves to the Dwemer, and eventually develop into the twisted creatures we see in-game. In truth, there were many other races that were once native to the frozen north of Tamriel, and Nords have no more right to call Skyrim their sole ancestral property than Argonians.
The Elder Scrolls V: Skyrim Special Edition is available on PC, PlayStation 4 and 5, and Xbox One and Series X|S