What is the function \usepackage[utf8]{inputenc} used for and why we should add this in latex document?

The inputenc package allows you to tell LaTeX about the input (file) encoding of your TeX document. The input encoding controls how the various characters you type are stored in your document (basically which sequence of zeroes and ones maps to which character). There are various input encodings (in the olden days, memory was precious and so you would only have characters in your encoding table that you actually used), so we needed a way to tell LaTeX how to interpret the file it reads. This is done by loading inputenc and passing the appropriate file encoding as an option.

Over time UTF-8 emerged as the de facto standard encoding for text files. Most editors use it as default when you write and save a new file. It is well supported across different operating systems and programs. That's why you will often see \usepackage[utf8]{inputenc} in TeX documents. People use the de facto standard and tell TeX about it.

In fact UTF-8 is so popular that the LaTeX team decided to make \usepackage[utf8]{inputenc} the default in LaTeX. Since the April 2018 release of LaTeX, LaTeX has automatically pre-loaded \usepackage[utf8]{inputenc}. That means that you no longer need to specify \usepackage[utf8]{inputenc} in order to use UTF-8 input. Some people still do, maybe out of force of habit, because they like to be explicit about the input encoding, or because there is a chance their documents need to run on outdated systems.

Some more details on input encodings and UTF-8 can be found at Is there any reason to use inputenc?.

Do note that while LaTeX now sets UTF-8 as default input encoding, full UTF-8/Unicode support is not something you can achieve with pdf(La)TeX due to technical limitations (I'm thinking combining accents). If you need full Unicode support, you may want to look into Lua(La)TeX or Xe(La)TeX.

A text file, like any computer file, is really made up of a series of numbers (usually collected as a series of numbers from zero through 255 called a byte). You need a set of rules (called an encoding) that can associate a character with a a set of these numbers. The UTF-8 encoding is such an encoding that has a set of rules that allows the characters associated with many languages (including mathematics, hieroglyphics, etc.) to be represented in a text file. When (La)TeX reads the file it has to ``know'' how to interpret the input bytes so needs to be told what encoding is being used. Recent versions of LaTeX default to using UTF-8 encoding (actually a sub-set of characters that can be represented by the font being used).