From Fallout lore, Vault 76 was one set to reopen 20 years after the nuclear war that set off the entire franchise. However, based on the alarm going off on the Pipboy, it is 27 October 2102, significantly earlier than the start date of adventures in Fallout 4 - 23 October 2287. It seems the survivor has lasted beyond those 20 years (the vault being called 76 because of the year it was created, 2076).
The trailer shows a lone survivor (well, no confirmation on the lone part of that) wandering through a seemingly deserted Vault, but a Vault in good condition. Party supplies cover the common space or cafeteria of Vault 76, the computer systems seem in good repair, and food is left on the table. If something happened, it happened recently. The sweet, sweet sound of John Denver's "West Virginia" plays over the radio, and we catch our first look at the golden lettering of the Vault suit. Gold for the tercentennial.
According to Kotaku, anonymous people "close to the project" say that this will be unlike the previous games of the franchise, likely an online survival RPG, and possibly multi-player.
Hopefully, alongside the introduction of Vault 76, we'll get a glimpse at Vault 77 soon too. I want to see a madman and his puppets. E3 really can't get here soon enough. We'll be paying close attention to whatever Bethesda brings to the show.