So my question is, what the heck does //= do?

This is the relatively new "defined or" operator

means that $a is unchanged if it is defined, and is assigned to $b if not defined.

At least, that's my understanding, I have never used it, but the following test under the Perl debugger seems to confirm it:

$ perl -de 42

Loading DB routines from perl5db.pl version 1.33
Editor support available.

Enter h or `h h' for help, or `man perldebug' for more help.

main::(-e:1):   42
  DB<1> $a //=5;

  DB<2> p $a
5
  DB<3> $a //=6;

  DB<4> p $a
5
  DB<5>
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