Official Mechanic:1/Turn

"1/Turn" (Japanese: ターン1回 Tān Ikkai) is a restriction to an ability to limit the use of the said ability to "Once per turn". In card text, the text is noted by a pink background with white text:  [1/Turn] /  [ターン１回]

Mechanics
As referenced in its name, the abilities is "Once per turn", and the restriction will only apply if its cost is paid. After you applied it once, you cannot apply it for the rest of this turn, even if the condition is met and you can pay the cost.

The restriction icon only exists in either  [ACT] ability or  [AUTO] ability.

AUTO
In AUTO abilities, the restriction will apply once both the condition is met and the cost is paid. If the cost is not paid even if the condition is met, the ability can be used later again that turn, provided the condition is met again.

Example
The text below is taken from the link provided in ref, but is modified to be used as a suitable example
 * Player A “Dragonic Overlord “The Legend”” on “Dragonic Overlord (Break Ride)” when he has 4 damage, and gain the Break Ride ability. “The Legend” then gained another AUTO ability due to its ACT ability, and attacked a rear-guard. Both AUTO abilities state “At the end of the battle that this unit attacked a rear-guard”, both abilities will activate at the same time, and the cost for the AUTO ability gained from “Dragonic Overlord” is chosen to be paid, “The Legend” [Stand].


 * During the second battle and it attacked a Rear-guard again, as “At the end of the battle that this unit attacked a rear-guard” is fulfilled again, he can pay the cost for “The Legend's” ability gained for itself, and [Stand] it again.