It's intended purpose is to reduce the memory load on your computer while working in very large assemblies, as @Anonymous described. Unfortunately, its most common actual use is probably by mistake by users that should have been using View Representations instead.
For whatever reason, when trying to hide a part, it seems like newer users very often find the "Suppress" option before they discover "Visibility". Both will remove the part from view. But Suppression is really a tool for memory management, and the invisibility should be thought of almost as a side effect, rather than the purpose of the setting. I suspect the reason is that new users carry the term "Suppress" over from other software, where it may have meant something a little different. Level of Detail (LOD) is simply a way of saving combinations of Suppressed components.
If you use LOD's where you don't need them, you will be opening yourself up to all sorts of annoying little problems. These problems are tolerable consequences if you actually needed the performance-boosting effects that the LOD is designed for. But if you're not hurting for computer performance, you're causing yourself trouble without gaining anything from it.
If all you are doing is hiding objects, Visibility and View Representations are the way to do it. Like LOD's are for Suppression, View Representations are a way of saving combinations of Visibility settings (and also color overrides).
LOD's are in some ways a relic of the past. In older operating systems (32 bit), they were often necessary to keep large or highly detailed assemblies practical to work in. With 64 bit operating systems, a model has to be huge to actually need them. Although I occasionally have to clean up some that were created mistakenly by newer users, we have not used LOD's intentionally at my company since about 2011. The largest assemblies that the company has ever created are still not large enough to need any LOD's on a modern computer.
There are also some applications for them in iLogic automation, where they are used as part of a technique for creating configurable assemblies. This has been an occasional exception to my rule of not using LOD's, though it hasn't come up often. LOD''s on their own (without programming code backing them up) are not useful as a configuration tool, and shouldn't be used that way if you value your mental health.
Bottom line, there is very little reason for you to use LOD's today. The exceptions would be if you are working on a model that is absolutely enormous, or if you are building some sort of iLogic smart model. But you do need to be aware of the possibility that users may have used them in the past for situations where View Representations would have been a better choice. Learning the basics of how to use them wouldn't be a terrible idea, in case you're ever faced with the prospect of needing to continue a previously-established convention of using LOD's in a particular assembly. But in general, you should avoid using them because they typically aren't needed anymore.