Not the one you replied but I was taught through university and books that functional programming's most important feature is the discouragement of side effects. Even on Wikipedia it's said to be a style of programming that "avoids changing-state and mutable data". I'd put discouragement of side effects and immutable data up there with higher-order functions (HOFs).

You're more than welcome to have your own definition, but it's my opinion that it's too broad since HOFs exist in some form in languages like Java and Ruby and I wouldn't call them functional though like another commented said, languages are mixing paradigms nowadays (with the exception of Haskell!).