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We first run into the test when Saavik is taking it. She ends up getting the Enterprise captured by the Klingons. Later on, she complains to Kirk (Vulcan-style) that there was no way to win, at which point Kirk gives the official answer: the scenario is meant to be "No Win," and the point is to determine how the candidate deals with an unwinnable scenario: how to carry on in the face of death and failure.

This is Layer 1.

We run into the test a second time when Kirk is "marooned" on the Genesis asteroid. At this point, Saavik (and the audience) believes that Kirk is stranded and the Enterprise is too badly damaged to fight: a No Win Scenario. She asks Kirk how he handled the test, at which point McCoy amusedly claims that Kirk is the only one to beat the Kobayashi Maru test: Kirk changed the parameters of the test to win (he cheated). At which point he reveals his trick: the Enterprise is NOT badly damaged, he is NOT marooned, the parameters of this situation are NOT a No Win Scenario, and he smirks confidently as he tells Saavik, "I don't like to lose," and bites into an apple.

This is Layer 2.

The test gets mentioned a third time at the end of the film. The Enterprise is unable to escape the Genesis blast, due to damage to the ship's engine core. The radiation level inside Engineering is so high that no human can survive it. As Kirk watches the clock run down, he suddenly gets word that the engines are back online. "Bless you, Scotty!" Because, of course Scotty would get the engines back online! He's Captain Kirk! He doesn't lo-- where's Spock?

Spock replies to Kirk with his answer to the Kobayashi Maru: Failure can't be cheated, but it can be mitigated. Logic dictates that the needs of the many outweigh the needs of the one. In the face of that logic, one's own death is not to be feared.

This is Layer 3.

Later on, while speaking to his son, Kirk admits what he's always known: he's never really taken the Kobayashi Maru test. He's always cheated or outsmarted failure and thought himself clever for it. This is his Kobayashi Maru test, where he has to carry on in the face of death and failure.

And so he does. Despite the loss he has suffered, he carries on. He reconnects with his family. Comes to terms with the loss of his friend. Acknowledges that new life comes in the wake of death. And although sorrowful, he moves on.

This is Layer 4.

And then we reach Star Trek III.

Kirk suddenly has a chance to cheat the Kobayashi Maru test again. He can outsmart the consequences of the No Win Scenario and get Spock back. After all, he's Captain Kirk, he doesn't lose. One quick trip to the Genesis Planet to retrieve Spock, and he can dodge the consequences of his failure again. . .