in reply to what is the meaning of $| in perl?

Now that you know what $| is, I suggest you don't use it! For Perl 5.8+, instead of your global LOGFILE file handle and: 

select(LOGFILE); $| = 1;
select(STDOUT);

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it is preferable to use a lexical file handle ($logfile say) and then simply: 
use IO::Handle;    # not needed for Perl 5.14+
# ...
$logfile->autoflush();

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Note that for Perl 5.14+ you don't need use IO::Handle because:

Before Perl 5.14, lexical filehandles were objects of the IO::Handle class, but you had to load IO::Handle explicitly before you could call methods on them. As of Perl 5.14, lexical filehandles are instances of IO::File and Perl loads IO::File for you.

Extra References Added Later

From On Interfaces and APIs:

Lexical file handles are, for me, the most important feature introduced in Perl 5.6. Those evil old global file handles spawned a host of unfortunate idioms, such as: 

select((select($fh), $|=1)[0]);

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In terms of a clear and simple interface to perform a simple task (set autoflush on a file handle), it doesn't get much worse than that, a compelling illustration of why keeping state in global variables is just plain evil ...

See also:

PM References

Unicode/UTF-8

In Section Seekers of Perl Wisdom