This is probably the raisin d'être of homoiconicity but it's more specific a concept than that. It's a conceptual property on the grammar of the language: there need to be control characters/words in the grammar like spaces and parentheses so that the parser can correctly generate nested lists, or trees matching the intended AST, even when it doesn't necessarily have full information about what the languages set of operative keyword are. Basically the parser has to support adding new, user defined operators.
And then in addition to being able to parse user defined operators, then you have to have a decently organized, simple system for applying AST transformations and modifying tree objects. And there again homoconicity in the grammar can be useful if it makes it easy to textually serialize and set object attributes.