$str =~ s/(.*)\|.*/$1/;

1. (.*) Matches and captures all characters, including  | (pipe) (but excluding, in this case, newlines), from the beginning of the string up to, but not including, the right-most pipe. The characters captured are stored in the  $1 regex special variable (see perlvar).
2. \|.* Matches (but does not capture) all characters from (and including) the right-most pipe to the end of the string.
3. Effectively, the entire string has now been matched.
4. /$1/ The replacement portion of the substitution: whatever has been matched is then replaced by whatever was captured in the  $1 capture variable.

Another way to look at this simple (i.e., up to Perl version 5.6, inclusive) match:

c:\@Work\Perl\monks>perl -wMstrict -le
"use YAPE::Regex::Explain;
 ;;
 print YAPE::Regex::Explain->new(qr/(.*)\|.*/)->explain;
"
The regular expression:

(?-imsx:(.*)\|.*)

matches as follows:

NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  (                        group and capture to \1:
----------------------------------------------------------------------
    .*                       any character except \n (0 or more times
                             (matching the most amount possible))
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
  \|                       '|'
----------------------------------------------------------------------
  .*                       any character except \n (0 or more times
                           (matching the most amount possible))
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
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See YAPE::Regex::Explain. (Note: This module is good only for version 5.6 and earlier regexes.) See also perlre, perlretut, and perlrequick.

Update: The regex discussed above will remove the right-most pipe character, but your OPed examples suggest you want to keep this character. If this is so, I would recommend the substitution posted by johngg here.