I have heard that static electricity from the human body can damage electrical components. Can you please tell me why this happens and what precaution I need to take so that I don't end up damaging computer components?

Internal computer parts and especially hard drives are extremely susceptible to static electricity. This static electricity is held within our body. It happens due to a process called Tribo electrification. Everything surrounding us including our body is made up of atoms.
The atom has a nucleus, which has protons positively charged and neutrons which are neutral.Outside the nucleus are the electrons, which are negatively charged.

The protons and neutrons don't change but the electrons transfer from one atom to another. When an object touches another object with either an opposite or neutral charge, electrons flow. Static electricity is created when electrons move back and forth between atoms.Before you begin work in the computer case, make sure you ground the static electricity.

There are two ways of doing it: Use an anti-static band (found in most of the electrical hardware stores). Touch the metal part of your computer case while it is plugged to the AC wall socket. The static electricity will be grounded through the wall socket.