A turning point is a specific, significant moment when something begins to change. Historians might say that Rosa Parks's famous bus protest was a turning point in the Civil Rights Movement.
Looking back at historical events, it's fairly easy to mark various turning points. An individual might notice a turning point as well, like the day you met your best friend or the summer you spent volunteering in India. This figurative meaning of turning point was coined in the 1640s, while a less popular, more literal meaning came along about forty years later: "point at which motion in one direction ceases and that in another or contrary direction begins."