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What is Hexadecimal for?

The hexadecimal, decimal, binary or octal bases are just different ways to represent a numeric value.

We are used to count using the decimal base: 0,1,2 ... 9, then 10 to 19, then 20 to 29 ... Using a hexadecimal base is just another way to count, we count from 0 to F, then we start again with 10 to 1f, then 20 to 2f ...
Octal and hexadecimal can be used to represent a binary value in different bases. It simply makes it easier to read! This is one of the reasons why we use it.

A hexadecimal value represents a group of 4 binary bits
Simple example:
Binary: 1001 1100 -> Hex: 9 c
A group of 8 bits is simply a bytes (octets). In computer system, we use bytes, which can be represented by two hexadecimal value:
Binary: 0000 0000 -> Hex: 00
Binary: 1111 1111 -> Hex: FF

For example, we can use hexadecimal in programming language (usually in low-level programming language) to represent the address of a variable in memory. It is simply easier to read than binary AND it represents the same value.
This is the same way for octal value. In that case it represents a group of 3 binary bits