Starships normally need to move forward x amount of squares before they can turn one arc on the hex map.
A garbage scow might need to move ahead 3 and then can turn one arc
A really heavy ship would be move ahead 2 then turn one arc
A speedy fighter would be move ahead 1 then turn one arc
And a tiny stunt flying ship would have a turn of zero, which means it can move ahead 1 and then turn two arcs
This mannuever lets you fly a gargabe scow like a heavy ship, fly a heavy ship like a speedy fighter, etc.
IIRC, Turn 0 means you can reorient your facing in any direction, not just two arcs.
If a starship has perfect maneuverability (the distance between turns is 0), the ship can make two turns for each hex that it moves (allowing it to turn around a single point).
straight from the core book.
From the rule book page 319:
Turns
While moving, a starship can make turns, altering its forward movement direction, firing arcs, and shield quadrants. One turn changes a starship’s forward facing by 60 degrees, or one side of a hex. Every round in which a starship turns, it must move a certain number of hexes before each turn, determined by its maneuverability (see the table below). For example, a ship with average maneuverability making two turns in a round must move at least 2 hexes before its first turn, and at least 2 more hexes before its second turn. If a starship has perfect maneuverability (the distance between turns is 0), the ship can make two turns for each hex that it moves (allowing it to turn around a single point).
The number of turns per round a starship can take is limited only by its speed and maneuverability. Turns don’t count against a starship’s movement speed. If a ship with average maneuverability has a speed of 8, it can usually turn a total of four times during a single round.
This means that if your starship had to move 2 spaces before it could turn, then it now only needs to move 1 space. Or if it needed to move a single space before it could make a turn, it now needs 0 spaces.