To put it briefly, the main difference between the two is that single quotation marks interpret and double quotation marks do not. So, when using single quotes, perl will assume that you want to print the exact characters between the quotes - excluding the slash single quote and double slash combinations.
# Example
# Single quotes
$book = 'Perl For Dummies';
print 'The title is $book.';
# Displays: The title is $book
# In contrast, double quotes
$book = 'Perl for Dummies';
print "The title is $book."; # note: only changing quotes around the print statement
# Now displays: The title is Perl for Dummies