Overhead refers to the amount of instructions it takes to process a certain block of php code.

In other words, it takes a server longer to process this:

echo "hello";

than it does this:

echo 'hello';

Granted on something that small it makes no difference. However if you were to use double quotes exclusively instead of single quotes on something like forum software, it all ads up and could make several seconds difference in loading time. Multiply that by thousands of users at a time and you've got a problem that could have easily been avoided by using propper PHP.