The function eof will return true after you've read all of the lines of the file. A simple example:

open FH, '<', 'file.txt' or die ("Can't read file: $!");

until( eof(FH) ) {
  print <FH>;
}
[download]

However, you rarely need to use eof() to accomplish what you are asking about. Imagine that you want read in a text file and, when finished, print the average length of lines (excluding any ending whitespace) to the screen, along with the number of lines. You might do that this way:

open FH, '<', 'file.txt' or die ("Can't read file: $!");

my ($lines, $total_length);

while (<FH>) {
   s/\s+$//s; # trims all traling whitespace, including \n
   ++$lines;
   $total_length += length($_);
}

#loop ends automatically when you reach EOF
printf "File had %d lines, with an average length of %d chars\n",
   $lines, ($total_length / $lines);
[download]

You see? You don't need to check for EOF by hand, as Perl does it for you.