Waves occur frequently in nature. The most obvious examples are waves in water, on a dam, in the ocean, or in a bucket. We are interested in the properties that waves have. All waves have the same properties.
Waves do not only occur in water, they occur in any kind of medium. Earthquakes release enough energy to create waves that are powerful enough to travel through the rock of the Earth. When your friend speaks to you sound waves are produced that travel through the air to your ears. A wave is simply the disturbance of a medium by moving energy but how is it different from a pulse?