The simplest and most common example of a hairpin turn is the turnaround in an out-and-back race. The most extreme example is what I consider my greatest moment in tactical racing.
If you look at runners approaching a turnaround in a race, you'll see the most common approach is to slow way down and take tiny stutter steps as close to the marker as possible. There are others that swing wide before the turn and cut in close after, those who cut in close before the turn and then have to swing wide and a few who take a very wide turn so they don't have to change pace. The most efficient way to do it is to pivot, an almost pirouette, a move that takes planning and practice - and only nets one a step or two over the competition. Before trying it, it's a good idea to do some shuttle runs, dashing back and forth between two arbitrary marks, to get accustomed to making changes in direction at speed; this is something that almost every sport demands, but which endurance athletes neglect. To do an ideal pivot turn, one plants the leg opposite the turn (left foot for right turn, right foot for lefts) directly past the turn point, leans into the turn, spins on the toes (or ball) of the planted foot and swings the other leg just past the turn and lands on it - facing the opposite direction. Explaining all the rotational forces and balance checks to do this is pointless; you just get a feel for it by practicing.
Beginners should simply plan how they'll do the turn before they get to it. If there's space, I prefer the wide turn with least decrease in speed as the best alternative.
Sharp turns are common in trail races. Frequently, the path going down a steep hill will zigzag and one also has to avoid tree roots, rocks and eroded ruts. Having to manoeuvre around other runners who are slowing adds to the obstacles. Practicing these turns at speed will help one deal with them in race situations.
My home course during college cross-country had a steep downhill close to the start, with a sharp turn at a tree at the bottom. Because the crowd had not thinned before this turn, this became a major tactical point of the race. To run free and clear of the crowd, one had to swing very wide on the turn; those who ran close to the tree ended up having to slow way down and wait for the runners in front of them as they found a way back into the stream of runners. After a few races, no one ran anywhere close to that tree and there was an open lane because people had learned it couldn't be run easily.
One day I figured out a solution. Before the race, my teammates saw me smearing Vaseline on the inside of my right arm; when they asked why, I said, "You'll know when it happens." The race started, we got to that hill and I ran way inside, on a collision-course with the tree. I threw out my arm, catching the tree, and was slung around it (nearly taking my arm out of the shoulder socket and scraping the skin off my arm despite the Vaseline), still moving at top speed and suddenly in the lead and way ahead of those in the middle of the pack I'd been running with. I could hear someone say, "Let him go. He's crazy." The leaders caught up with me quickly, but I'd gained an advantage over the runners of my calibre - and a reputation.