The origin of suffering is craving, and the extinction of suffering is stopping craving. It doesn't follow, logically, that removing the cause removes the effect. Here, Gotama is clearly saying that in this case removing the cause of suffering, craving, removes the effect, suffering. So, he claims, the mental experience of painful suffering (as opposed to suffering by definition) is, according to this truth, maintained by craving. And suffering goes away when craving stops.
If we experience removing suffering by removing craving, we gain some experience of a state beyond suffering, or Nirvana. When we let go of craving and experience the resulting relief and happiness, we get an idea of a better way to exist. This third truth is Nirvana.
A wave appears to move across the water − apparently coming to be, rising, falling and disappearing. It is propelled by forces (such as the wind, and other currents). When these forces occur, the wave occurs. And when these forces abate, the wave ceases (eventually). In the same way when craving stops, suffering stops.
As we learn that by stopping suffering, we stop craving, we can, at that time, experience the possibility of life without suffering. That is we get a hint of enlightenment and Nirvana.
The wave image is also used to illustrate the continual birth and rebirth. The wind blows, and waves are formed. The wave (the being) comes into existence, grows, ages, and dies. And the new wave symbolises the new being coming to be and ceasing to be. The wind is a symbol for craving.
Ultimately, the Buddhist extinguishes craving, so the wind ceases to blow and the water is calm and serene. The Buddhist then enters Nibbana (Nirvana), which literally means blown out.