Wight Hunt

The ranging from Eastwatch-by-the-Sea is undertaken by the King in the North Jon Snow and his allies in order to provide proof to Queens Cersei Lannister and Daenerys Targaryen of the existence of the wights and their masters, the White Walkers, led by the Night King, who had risen again after 8,000 years.

King Jon was accompanied by his principal advisor, Ser Davos Seaworth, wildling chieftain Tormund, Robert Baratheon's bastard son and Davos's friend Gendry, and Ser Jorah Mormont of Daenerys's Queensguard, traveling to Eastwatch-by-the-Sea from Dragonstone. There, they also joined forces with the Brotherhood Without Banners, including Lord Beric Dondarrion, Thoros, and Sandor Clegane, which had marched north from the Riverlands to help play a part in the war against the White Walkers, having been guided by visions.

Prelude
See main articles: Long Night and Conflict Beyond the Wall

At the dawn of the Age of Heroes around 8,000 years ago, a dark and cold winter fell upon the world known as the Long Night, lasting for more than a generation. In that winter, the White Walkers, led by the first White Walker, the Night King, descended upon Westeros for the first time, sweeping through villages and towns and slaughtering all in their path, raising the corpses they made as wights to serve in their army of the dead. Eventually, however, the First Men and the Children of the Forest banded together and defeated the White Walkers in the War for the Dawn. As the centuries passed, both the White Walkers and the Children seemingly disappeared, and were assumed by most to have been nothing more than legends and fewer to simply be extinct, with magic gone from the world.

Nonetheless, in the years surrounding Robert's Rebellion and the War of the Five Kings, the White Walkers had risen again with the Night King leading them. They massacred the Free Folk living beyond the Wall, which had been raised by the First Men and guarded by the Night's Watch to prevent the White Walkers from invading southern Westeros again. Though they had been bitter enemies for centuries, the Night's Watch and the Free Folk ultimately banded together to face their common enemy under Lord Commander Jon Snow.

Jon went on to face a mutiny but was resurrected by Melisandre at the urging of Ser Davos Seaworth. With Sansa Stark, Jon defeated House Bolton in the Battle of the Bastards, seeking not only to restore House Stark's control on Winterfell, but also to unify the North to face the resurgent army of the dead when they came. Jon was subsequently declared the King in the North by the lords of the North and the Vale, seceding from the Seven Kingdoms once more and reviving the Kingdom of the North.

However, when Daenerys Targaryen began her invasion of Westeros, King Jon decided to treat with her at Dragonstone, where she controlled the mines of dragonglass, which could be used to kill White Walkers and wights. Daenerys was also the "mother" of three fire breathing dragons that could be used to burn wights in the thousands. After reading a reconnaissance report from Bran Stark, the new Three-eyed raven, concerning the movements of the army of the dead, Jon and Tyrion Lannister were ultimately able to convince Daenerys, who had insisted Jon bend the knee to her, to allow the King in the North to travel to Eastwatch-by-the-Sea to capture a wight to use as proof of their return and existence for her and Cersei Lannister, the queen who sat on the Iron Throne and the primary opponent of Daenerys Targaryen in her war.

At Eastwatch, King Jon, who was accompanied by Ser Davos, Gendry, and Ser Jorah Mormont, met with wildling chieftain Tormund Giantsbane to discuss this mission. Tormund brought them down to the ice cells where he held prominent members of the outlaw group the Brotherhood Without Banners prisoner, including the leader Lord Beric Dondarrion, the red priest Thoros of Myr, and Sandor Clegane. Despite their differences and somewhat distrusting of each other, they all agreed to come together and accompany King Jon and his allies on their mission to capture a wight beyond the Wall.

The mission
The mission will be depicted in "Death Is the Enemy."

In the books
In the A Song of Ice and Fire novels by George R.R. Martin, such a mission will not occur. In the Inside the Episode video for "Eastwatch," showrunner D.B. Weiss admits that the wight-hunt that Jon is going on is an invention of the TV series, an idea "we came up with" which isn't based on events in a future novel.

For that matter, he says that it's loosely inspired by how Alliser Thorne was sent to King's Landing with the severed hand of one of the two wights that tried to kill Lord Commander Mormont, to present it as proof their claims were real, but it rotted away to nothing by the time he was granted an audience. This did not happen in the TV version - it happened in the books, but was omitted from the TV series (though the way the video is edited, it seems that Weiss was explaining that this drew inspiration from that section of the books, not specifically claiming he thought they did it that way in the TV series as well).