A double eviction happens on a Thursday night right after the standard weekly eviction occurs. Normally, houseguests have the week to win a Head of Household competition, select nominations for eviction, play a Veto game, and then vote on who they want gone.
With a double eviction, all of that is done in the span of one episode.
Yes, it's as wild and as fast-paced as it sounds. This usually makes it so the houseguests don't have much time to strategize or talk to their allies when putting up players for eviction or voting on them after.
So when the double eviction happens on Big Brother, houseguests will then be thrown into the HOH competition, followed by a nomination ceremony. After that, they'll play Veto. Then, voting happens. It's a week of action in one episode.