One definition of survival instinct is to do things in a dangerous situation that will save us from dying.

This is linked to the instinct of self-defense and self-preservation in dangerous situations.
Now let's take a look at our performances in sports. How often did we feel exhausted, but we still were able to continue? The simple example of pushups: at the end of our max, we feel like we are not able to move at all, but some factors can motivate us to do one or two more.

Same results with the study measuring soldiers' performances when alone, or when observed by a ranking officer. In the second situation, their performances were higher.

The point here is to be conscious that our exhaustion point is not fixed at all. It is a limit we define depending on the situation.

Other explanations could be provided as well, but here, I would like to focus on our survival instinct. This instinct asks us to be able to react if the situation is dangerous. So if a lion shows up, we have to be able to run away, even if it is at the end of a marathon. This is our instinct and it is very deep.

So we are designed to keep enough strength to be able to do things at any given time. It means our real exhaustion limit is far higher than our perceived limitations. I am not saying every time we train, we should train till we fail. But we have to keep in mind our initial limit when our body says it is too much, it is often just a protection in order to keep enough energy in case a predator shows up.

So next time we go training, and when it becomes hard, we just have to realize, we are only at the "I am still quite ok" zone.

Now everyone has to meet his "lion", meaning internal or external motivations, to go beyond his limits and boundaries.