What's the difference between use and extern?

extern crate foo indicates that you want to link against an external library and brings the top-level crate name into scope (equivalent to use foo). As of Rust 2018, in most cases you won't need to use extern crate anymore because Cargo informs the compiler about what crates are present. (There are one or two exceptions)

use bar is a shorthand for referencing fully-qualified symbols.

Theoretically, the language doesn't need use — you could always just fully-qualify the names, but typing std::collections::HashMap.new(...) would get very tedious! Instead, you can just type use std::collections::HashMap once and then HashMap will refer to that.

The accepted answer was correct at the time of writing. It's however no longer correct. extern crate is almost never needed since Rust 2018.

You're now only required to add external dependencies to your Cargo.toml.

use works the same as before.

Read more in the official documentation.

Edit: The accepted answer has now been edited to correctly reflect the changes in Rust 2018.