What does it mean when a state flag is flown upside down?

It depends. In some countries it is a distress signal, in some countries it is frowned upon (Australia for instance) while the Philippines military use the national flag upside down as a war flag (and is the only country to do so). In some instances (some international events!) flags are flown upside down because of ignorance or stupidity. This has been known to happen with the Union Jack, which, while it looks symmetrical, is not, and easy to hoist incorrectly.