I would hazard that this means closures that can capture (shared) state. In Rust, a closure’s data must either be moved into the closure or outlive the closure (dangling pointers etc etc). In most other languages, GC allows closures to keep a handle to any data at all.
Exactly - sharing is the core of FP
If you want a closure to outlive the outside bindings of its captures and thus have shared control over their lifecycle (which is the default behavior of closures in most FP languages) you can easily use Rc<> or Arc<> to that effect. Rust just forces you to be explicit about it.