In BB1-5, Double Eviction weeks fundamentally worked the same as a regular week, the only difference is 3 people are nominated instead of 2. At the eviction ceremony, 2 of the 3 nominated houseguests will be evicted.
From BB9 on however, the second half of the week would have a live HOH competition, nomination ceremony, POV competition, POV ceremony, and eviction ceremony all in a couple of hours. This would result in 2 people joining the jury in 1 night.
Effects on the Game
The twist ultimately does nothing more than speed up the game, and grants the current HOH much more power in choosing 2 players to evict. In BB9, the current HOHs do not receive more power as there are now 2 of them.
The 3-nomination way of eviction is an old version of the Double Eviction, and has not appeared in the last few seasons, as hosting has shifted towards Discord from the PokéBeach forums.
The live double eviction, though new to the series in execution, is likely to stick around as a twist.