I'm unsure exactly what you're looking for.  Yes, most likely there is a
background thread there, and probably some synchronization using
wait/notify so that when the code is changed, the environment can run it
against the syntax and semantic checkers.

Not that in general, the IDE doesn't actually compile as you type.  It
just runs the first few stages of the compiler -- lexical, syntactic,
and semantic analysis, and reports any errors.  Eclipse, at least, also
stores the abstract syntax tree that results from the parser (syntactic
analysis), so that it can be used by various plug-ins to interact with
the source code at a higher level than plain text.