For Multiplayer & Escalation, the person instigating a game is labelled as "the host". Even though the game isn't being hosted at their home/console, the Playstation Servers make it so that the game "belongs" to that person who instigated it... so if that person logs off or has a connection drop-out, it would terminate the game and kick off everyone else in it (meaning a loss of points and time to your score).
Host migration was introduced to not terminate the game when the instigator leaves - instead, it would then shift the hosting status to someone else... allowing for the game to continue.
Personally, I don't understand why a game needs to be "hosted" by an individual if the Playstation Server is actually hosting the game. Maybe it's just the way they originally wrote the programming... and can't/won't change it to avoid the need for host migration. (seems like the wrong sort of fix to a problem they didn't need to have in the first place)