Question

I am confused about the differences between grep, awk and sed in terms of their role in Unix/Linux system administration and text processing.

Answer 1

Short definition:

grep: search for specific terms in a file

#usage
$ grep This file.txt
Every line containing "This"
Every line containing "This"
Every line containing "This"
Every line containing "This"

$ cat file.txt
Every line containing "This"
Every line containing "This"
Every line containing "That"
Every line containing "This"
Every line containing "This"

Now awk and sed are completly different than grep.
awk and sed are text processors. Not only do they have the ability to find what you are looking for in text, they have the ability to remove, add and modify the text as well (and much more).

awk is mostly used for data extraction and reporting. sed is a stream editor
Each one of them has its own functionality and specialties.

Example
Sed

$ sed -i 's/cat/dog/' file.txt
# this will replace any occurrence of the characters 'cat' by 'dog'

Awk

$ awk '{print $2}' file.txt
# this will print the second column of file.txt

Basic awk usage:
Compute sum/average/max/min/etc. what ever you may need.

$ cat file.txt
A 10
B 20
C 60
$ awk 'BEGIN {sum=0; count=0; OFS="\t"} {sum+=$2; count++} END {print "Average:", sum/count}' file.txt
Average:    30

I recommend that you read this book: Sed & Awk: 2nd Ed.

It will help you become a proficient sed/awk user on any unix-like environment.