What are .in files?

I believe the automake process involving a Makefile.in is something like this:

  Makefile.am
       |
      \'/
+--------------+
|   automake   |
+--------------+
       |
      \'/
   Makefile.in
       |
      \'/
+--------------+    +--------------+
| ./configure  |<-- |   autoconf   |<-- configure.in
+--------------+    +--------------+
       |
      \'/
    Makefile

Nobody actually writes a Makefile.in. The only programmer-defined file here is the Makefile.am.

it's just a convention that signifies the given file is for input; in my experience, these files tend to be a sort of generic template from which a specific output file or script results.

They are input files for the m4 macro preprocessor. Among other things, these files contain macros marked by @, that get expanded by m4.