The horizontal axis is time, but it's bidirectional. As you get more sleep, you move to the right on the curve, while you're awake, you move to the left. The vertical axis measures how rested and alert you are. The general trend is as you would expect: as you get more sleep, you're more awake, aware, useful, and happy. Point A, at the upper right, represents the state of being fully rested.
However, it's not a simple, monotonic, curve. It undulates, rather a lot. The peaks (local maxima) represent times when it is easy to wake up. The troughs (local minima) represent times when it is easy to fall asleep. The ideal situation is to live along slope B, waking up at A fully rested, drifting down B during the day, and reaching C at bedtime, thence to climb back up B whilst asleep, returning to A when it's time to start the next day.
But it's more involved than that. If you stay up too long, you eventually wind up at D, which represents your "second wind", when you're feeling pretty good, even after being awake too long or after insufficient sleep. This also illustrates why sometimes, when you've had a night's sleep, you end up feeling more tired than when you began; you've simply slept from D to C, you've knocked back your sleep debt, but you've wound up on the wrong end of the curve.
Some people end up staying at D and not realizing it, never achieving their full potential, similarly to people who go around dehydrated all the time. As you accumulate sleep debt, you slide back on the curve, reaching the less pleasant points at E or even F. I suspect that there are health costs to this as well.
There's actually some sort of fractal effect going on as well, that I've somewhat glossed over. In a normal night's sleep, most people would cover several oscillations. This is reflected in sleep studies, where people get their deep sleep in chunks, starting with shorter periods and progressing to longer ones toward morning. This is reflected in the graph, as the cycles to the right are longer than the ones to the left. When people get up early, before they're fully rested, they don't reach "A", but climb out of bed at D or E. Or, if the alarm cat goes off at the wrong moment, people can end up trying to wake up at B or C, which is much more difficult.