I'm guessing that compiled code loads faster, though for typical plugins, the difference is probably negligible.
I can't think of any other benefits, though perhaps someone else can.
This is from the lua.org luac manual page, which does provide a brief discussion of the advantages of precompiling:
The main advantages of precompiling chunks are: faster loading, protecting source code from accidental user changes, and off-line syntax checking.
Precompiling does not imply faster execution because in Lua chunks are always compiled into bytecodes before being executed. luac simply allows those bytecodes to be saved in a file for later execution.
Precompiled chunks are not necessarily smaller than the corresponding source. The main goal in precompiling is faster loading.
I hope that answers your question. Off the top of my head, I'd have really just said, "What John said" … but I guess there are some other (minor) advantages....
Do bear in mind that the page also discusses what might be a disadvantage of precompiling your lua source:
The internal format of the binary files produced by luac is likely to change when a new version of Lua is released. So, save the source files of all Lua programs that you precompile.
In any event, I think it should be pretty obvious that if you compile your code, you want to make sure to keep your original source code safely tucked away where you still have it for any fixes and/or for recompiling (with a newer version of luac) or for reading and refactoring/translating (in the event of a total technology shift).