Please explain this BASH code (one line)

It means use $PIDFILE if $PIDFILE is defined, or /var/run/service.pid if $PIDFILE is undefined.

Starting with a new shell:

$ echo ${PIDFILE-/var/run/service.pid}
/var/run/service.pid

Now define PIDFILE:

$ PIDFILE=/var/run/myprogram.pid
$ echo ${PIDFILE-/var/run/service.pid}
/var/run/myprogram.pid

It is from the old days of Bourne Shell sh man page.

   ${parameter-word}
          If parameter is set then substitute its value;
          otherwise substitute word.

The other form you might have already seen is ${parameter:-word}. It is similar, but behaves differently if parameter is set to the empty string.

   ${parameter:-word}
          Use Default Values.  If parameter is unset or null,
          the expansion of word is substituted.  Otherwise,
          the value of parameter is substituted.

To demonstrate:

$ set | grep NOSUCHVAR    # produces no output because NOSUCHVAR is not defined
$ echo ${NOSUCHVAR-default}
default
$ echo ${NOSUCHVAR:-default}
default

$ NULLVAR=
$ set | grep NULLVAR      # produces output because NULLVAR is defined
NULLVAR=
$ echo ${NULLVAR-default}

$ echo ${NULLVAR:-default}
default

Note how ${NULLVAR-default} expands to the empty string, because NULLVAR is defined.

For a full explanation, run "man bash" and search for Parameter Expansion by typing "/Parameter Expansion".

The ${parameter-word} bit is hidden away in this explanation:

    When  not  performing  substring  expansion, using the forms documented below,
    bash tests for a parameter that is unset or null.  Omitting the colon results
    in a test only for a parameter that is unset.

Thanks to Dennis for the correction about set versus null.

Mikel:

shouldn't it be pidfile=${PIDFILE:-/var/run/service.pid} the way you are explaining?