As an example, here are two roughly equivalent programs. First Rust:

    let x = Box::new(5);
    let y = x;
    println!("{}", x);

Now C++:

    unique_ptr<int> x(new int(5));

    auto y = std::move(x);

    cout << *x << endl;

(I'm being a bit sloppy with namespaces, and both need a main(), but you get the idea)

Here, the C++ will compile and (probably) segfault, as x is nullptr after the move. The Rust will fail at compile time, with "use of moved value."

Basically, a (possibly over-)generalization of the situation is "Rust is move by default and captures errors at compile time, C++ is not move by default and cannot statically prevent as many errors as Rust can."

It's not identical (Rust statically enforces a lot more than C++ does, move semantics are opt-out rather than opt-in, there's no such thing as move constructors in Rust, etc.), but if you understand unique_ptr then you'll understand Rust's concept of ownership.