While we don't know much about the War of the Dead Zombies map, a bit about the related story has been rumored. Vanguard is being developed by Sledgehammer games, who have worked on other Call of Duty titles like Modern Warfare 3 and Advanced Warfare. But the Zombies mode for Vanguard is being spearheaded by Treyarch.
Many players were delighted by that news, believing that Treyarch has a better vision overall when it comes to Zombies. Besides personal preferences, Treyarch working on Zombies also means they will probably continue their own storyline.
The Call of Duty: Black Ops Cold War Zombies story centered around the Dark Aether. The Dark Aether is essentially a hell dimension where the Apothicons — an ancient, villainous, and tentacled race — were banished. In a convoluted series of events, the Dark Aether began infecting Earth. Through the events of Zombies, players work to fight back against the invasion.
Treyarch will most likely continue on with the Dark Aether story, potentially even designing the Vanguard maps to be prequels for the Cold War ones. Given that Vanguard is set decades before Cold War, this adds up. The Apothicons were originally brought to Earth through Projekt Endstation during World War 2, lining up the timeline perfectly.
Maps in Zombies mode traditionally have rounds, with each one progressively becoming more challenging. Cold War broke from this format in Season Two, introducing Outbreak mode. Outbreak is a Zombies mode that sees players beat a series of objectives as opposed to just surviving. It looks like Outbreak, and also Onslaught, will be returning in Vanguard. TheMW2Ghost stated that an Outbreak and/or a Onslaught map, or a combination of the two would be available when the game releases.