This term really caught on with people who develop for the web because there actually is a divide here: some people really prefer the front-end work (JS/HTML/CSS), some people prefer the backend work (sysadmin/app logic/data stores) and some people prefer both.
So basically, if someone says "full stack", they likely mean that you can develop and run the entire product, not just a part of it.
Having said that, I strongly encourage everyone to go deeper. Learn some C. Figure out the difference between a function and a syscall. Understand what the kernel does and how it works (whichever kernel you happen to use). Write a toy libc. Program for a microcontroller (try adding RAM to a microcontroller circuit for added fun). Play some Minecraft. Write a bit of assembly. Create a data store. Develop a JS framework for DOM manipulation. Create a toy programming language. Write a malloc implementation. Write a kernel module (maybe a driver to that microcontroller device you put together). Write a web server. I find that the more of this kind of stuff you do, the more aware you become of what `display: block;` will do and how to structure your code better.