While the affected realms will remain technically independent, the lines between the two connected realms will be blurred. These realms will be able to share population, have one linked auction house, and allow players of both servers to group, guild, and PvP together.
So why not just merge? Blizzard's official answer reasons, "Other alternatives such as merging realms would require us to force character name changes if there were conflicts, and could lead to confusion for returning players who'd log in to find their realm missing from the realm list. Some players also feel strong ties to their realm's name or history, and we don't want to erase that."
The list of what servers will be connected has yet to be released.