We can see waves travelling through water. There are many sorts of these waves, such as ripples, swell, tsunami, and even sound waves that we do not see, but we hear if our ears are under the water.
Likewise, many different types of waves can travel through the air. We detect one type with our eyes as colours; we detect another type when it lands on our skin, as warmth; another type is called X-rays. Other types of these invisible waves are called microwaves.
We cannot see them. They can quickly penetrate quite deep into materials that contain water, for example most food. The energy in these waves makes the water molecules vibrate faster, which means the water gets hotter.
Although they can also heat some metals, there are materials, including many plastics, which they pass right through, without heating at all. Although many plastics used in bowls or cups will melt and get super-heated in microwave ovens.