What is S.H.M.?

A body executes SHM when its acceleration is directly proportional to its displacement but in the opposite direction.

OK, this is the formal definition of SHM which probably doesn't mean a great to you at this point. Basically SHM is an idealised time of oscillating motion. If an object is vibrating / oscillating then scientists can analyse its motion and make predictions about it by assuming that it is oscillating with SHM. Its motion may not be exactly SHM but, in most cases, it will be a reasonable approximation.

There are many objects, both man-made and in nature, which oscillate. Using the equations you are about to learn we can describe their motion and make useful predictions.

Here are some examples

Galileo realised that pendulums oscillate with a constant period and that this could be used in devices to keep time. A simple pendulum is just a mass suspended on a string.
When designing bridges and other structures possible vibrations have to be taken into consideration. After the Millennium Bridge in London was built it was found to oscillate unacceptably. Soldiers are taught to march out of step when they cross bridges in case the vibrations produced destroy the bridge.
Machinery which contains moving parts is prone to vibration. If you don't believe me sit on your washing machine. The springs in a cars suspension give a smooth ride when you go over bumps but shouldn't be too bouncy.
Quartz crystals vibrate at very precise frequencies using electric fields. Does your watch have a quartz crystal in it?
Wind passing over a sax reed makes it vibrate. This makes the air inside vibrate. A standing wave is set up and beautiful music is made.