Speaking about a real-world example, there are several reasons to use multi-threading, and I wouldn't hire a web-developer who doesn't know about it. But in the end, the reasons to use multi-threading are the same for standard- and web-development: you either want something that take a while (aka blocking) done in the background to give the user some response in between, or you have a task that can be speed up by having it run on several cores. When multi-threading is actually useful is however a different question.
Situation 1: A web server that does require some processing and has low hits/second
Here multi-threading (if applicable to the algorithm) is a good thing, as idle cores are utilized and threading can result in a faster response to the user.
Situation 2: A web server that does require some processing and has high hits/second
Here multi-threading is possible, but as cores are usually busy with other requests, there are no resources left to use it properly. Actually spreading out the task to several threads can even have a negative impact on the response time, as the task is now fragmented and all parts need to complete, but the order of execution with threads is undefined. So one client could immediately receive a response, while others might wait into time-out till their last fragment eventually gets processed.
Situation 3: A web server has to do some processing that takes a very long time
Here multi-threading is required, there is no way around it. A client cannot wait minutes or probably hours till it receives the response. In this case a callback system is usually implemented, so basically each task has an "API" that can be queried for the current state. Most online-shops are an example for this: you order something and later you can query your order status.
The alternative to threading is process-forking, as Apache does in its standard configuration. The benefit is that load is spread across cores (mostly applicable to situation 2), and the web-code itself doesn't have to do anything to use all those cores, as the OS handles that automatically. However if you have imbalanced load, some cores can be idle and resources are not used in an optimal way. A threading situation is almost always the better solution, if it is done right. But the Apache/Tomcat standard configuration uses a very outdated threading model, by spawning one thread for each request. Effectively given a certain amount of hits/second, the CPU is more busy with threading than with actually processing those requests.