I see the answer has already been chosen here and perhaps this is something you are already aware of but for what it's worth I'll give my two cents for a simple use case of fuzzing.
Fuzzing has a variety of applications, some already explained in the above-posted answers and comments, though I have used it for other cases as well. An easy example of fuzzing, though some might view this as scanning, would be taking a wordlist of potential directories or file names and searching them on a domain you are allowed to investigate. Tools like dirb and gobuster, among others, might be worth taking a look at if you are curious how this type of fuzzing can be done.
gobuster
example command below to enumerate test.com:
gobuster -u https://test.com -w ~/wordlists/shortlist.txt
In short, the bugs discovered in this case with these tools are often directories and files that are publicly viewable (though should perhaps not be). This enumeration can lead to discovery of interesting things to aid an attacker in further exploitation.