Record of Agarest War is now out! Go buy it!
Download the user manual here.
There are two kinds of turns in the game: turns for each generation and turns for the entire game. Each affect events. For the total number of turns, keep in mind whether the number is high or low.
Turns for each generation sometimes affect the conditions for key story events to occur.
If you hear online about events not mentioned here, just make sure to check if you're required to have a certain party member and your number of turns.
You'll encounter special events as you go that are outside of the main story.
The conditions required for the special events to occur vary from easy to complete, to challenging multiple-step processes.
Taking too many detours makes it harder for events to occur in general.
But, if you aren't concerned with getting the special events, you don't have to watch your turns as closely.
In any case, if you focus too much on the turn system, you might not be able to enjoy the game. So try to follow your own play style.
For those who want to view every event in one play-through, please refer to the walk-through here, or those on other online sources.
It's not a stretch to say the link gauge exists for the special events. The gauge affects branch points of the main story as well, but its main role is to decide whether special events occur or not.
The rule of thumb is to avoid keeping it heavily on one side or the other.
But, that doesn't necessarily mean keep it in the middle. It's best to have it in a position where you can easily make adjustments during tide-turning events.