What are things desktop applications do that web apps can't?
For example: controlling the mouse, which can't be done from a browser for security reasons.
Well, you can streamline & integrate an entire office's financial, scientific, engineering, marketing, sales, recordkeeping, paperwork, HR, and internal communication and it can be done with the utmost security & reliability when there is no wireless and no connection to the web whatsoever.
Heavyweight media creation applications; eg. Blender/ZBrush, Substance Designer/Painter, Avid MC, ProTools, Adobe Premier/AfterEffects, UE4 Editor.
I always get a chuckle out of web programmers who think that because they can do their entire job out of a few web apps, that everyone else can too.
Fully interact with the operating system API/SDK, not just a subset of it.
Process extremely large amounts of local data quickly.