I rewrote this fairly quickly, putting comments inline. It works, but the thing to consider is that a lot of the changes were stylistic changes. Other monks may have cleaner/better solutions.

#!/usr/bin/perl -w

use strict;
my $in = (); # usr input
my $exit = 'n'; # done yet?

my %acro = (
    'HTML' => "Hypertext Markup Language",
    'ICBM' => "Intercontinental Ballistic Missile",
    'EEPROM' => "Electronically-erasable programmable read only memory
+",
    'SCUBA' => "Self Contained Underwater Breathing Aparatus",
    'FAQ' => "Frequently Asked Questions",
    'LCARS' => "Library Computer And Retrieval System",
    'NASA' => "National Aeronautical and Space Administration" 
             );

# I personally don't like empty conditions on
# while loops.  This changed the logic a bit, so
# I changed the exit prompt as well.
while ($exit !~ /^y/i) {
    print "\nPlease enter an acronym: ";
    chomp($in = <STDIN>);
    print "\n";

    # I'm lazy, and don't want to worry about entering
    # uppercase acronyms.  The uc() changes input to
    # uppercase automagically.  Also, this approach
    # doesn't loop over every key every time.  That's
    # what a hash is best for -- so you don't have to loop
    # over everything.
    if (exists $acro{uc($in)})
    {
        # No need to assign to a temp variable, btw.
        print "$in is the acronym for ", $acro{uc($in)}, " \n\n";
    }
    else
    {
        # I also echo input so if the user mistyped the acronym they
        # may see the error.
        print "Sorry. But $in is not an acronym that I recognize!\n";
    }

    print "\nFinished? ";
    # Your original script didn't have any way to input $exit, so
    # it went into an infinite loop (I am guessing that was a
    # transcription error)
    chomp($exit = <STDIN>);
}
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Ask if any of this doesn't make sense.

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