Imagine two walls :

| | | | | |Now how many vibrational modes can you fit between the two walls ? This is the question that was asked when people tried to calculate the energy spectrum that a heated object should emit. Back in the day before quantum mechanics the world was considered continuous. This means that you can divide the seperation between the walls into an infinite set of modes. Each mode contributes equally to the energy and as your number of modes diverges so does the energy that you expect to see coming out of the heated object. This is the ultraviolet catastrophe. Planck set a limit to the smallest size of the modes. He quantized the system. This was the first introduciton of quantization into physics. He did it in 1905