This is about who mounts the content to display.
If it is on the server it obviously has all the work of putting together text that will be the page to be delivered to the client essentially ready for use.
If it is on the client, a set of page plus miscellaneous codes will be received by the client and from there it will only communicate with the server to request new information that it needs, everything that needs to modify and adapt in the presentation of the page occurs in the client even.
There are hybrid cases.
Obviously drawing everything on the client may slightly unload the need for the server to work. In theory, because depending on the case making multiple requests alone can generate so much load that it can be worse than rendering on the server. Not to mention that the developer can do everything wrong and make things worse.
Rendering on the client can bring more insecurity, breach of privacy, piracy of the code. Of course most of these things can be solved with some work.
Rendering on a client does not usually go very well with SEO, even if some people believe that it does not have a problem, that is, it's not very good for websites. It works better and has more advantages in web applications that are very different.
As unbelievable as it sounds, there is not as good control rendering on the client, at least in the current state of technology.
I need to leave, I'll finish later.