The first barrier is the pain felt because you're running at max performance. This is all mental, and you learn to love it. The mental barrier grows exponentially more difficult to fight as you get closer to...
The second barrier. The true hard limit, as defined by your body's innate physical capacity to perform. At this point you've managed to push past the mental barrier and used up every ounce of energy. It's typically marked by a visible decrease in performance aka "hitting the wall". I've done it before, and there is no amount of mental convincing that will get the body moving when there is no more fuel in the tank. This shutdown might be a protective function of the brain (as a physical organ) looking to ensure it can still function, but there really is no physical capacity left to continue at speed even if the will is there.
Any true athlete intuitively knows from their training when that second wall is approaching and will time it as best as possible so that they get as close to it as possible just as they finish their performance (hence running faster at the end). This is much more evident in endurance events where blowing past the anaerobic threshold too early is disaster for the competitor.
One of the best events to watch athletes hit the second wall is the 800m.