Waves and Wavelike Motion
Waves occur frequently in nature. The most obvious examples are waves in water on a dam, in the ocean, or in a bucket, but sound waves and electromagnetic waves are other, less visible examples. We are most interested in the properties that waves have. All waves have the same basic properties, so by studying waves in water we can transfer our knowledge and predict how other types of waves will behave.
Waves are associated with energy. As the waves move, they carry energy from one point to another in space. It is true for water waves as well. You can see the wave energy working while a ship drifts along the wave in rough sea. The most spectacular example is the enormous amount of energy we receive from the sun in the form of light and heat, which are transmitted as electromagnetic waves - not even requiring a medium to propagate.
Simple Harmonic Motion
Simple Harmonic motion is a wavelike motion. It is considered wavelike because the graph of time vs. displacement from the equilibrium position is a sine curve.
An example of simple harmonic motion is a mass oscillating on a spring. It will be hard to understand the forces involved this early in the course that cause the motion to simple harmonic, but it is still possible to look at a mass oscillating on a spring and understand that it is indeed simple harmonic. When a mass is oscillating on a spring, the further the string stretches, the slower the mass will be moving. Then the mass reaches a point where the string won't stretch any further, so it quits moving and then it reverses direction. As it moves closer to the equilibrium position is moves faster.