What's the difference between placing "mut" before a variable name and after the ":"?

If you're coming from C/C++, it might also be helpful to think of it basically like this:

// Rust          C/C++
    a: &T     == const T* const a; // can't mutate either
mut a: &T     == const T* a;       // can't mutate what is pointed to
    a: &mut T == T* const a;       // can't mutate pointer
mut a: &mut T == T* a;             // can mutate both

You'll notice that these are inverses of each other. C/C++ take a "blacklist" approach, where if you want something to be immutable you have to say so explicitly, while Rust takes a "whitelist" approach, where if you want something to be mutable you have to say so explicitly.

mut foo: T means you have a variable called foo that is a T. You are allowed to change what the variable refers to:

let mut val1 = 2;
val1 = 3; // OK

let val2 = 2;
val2 = 3; // error: re-assignment of immutable variable

This also lets you modify fields of a struct that you own:

struct Monster { health: u8 }

let mut orc = Monster { health: 93 };
orc.health -= 54;

let goblin = Monster { health: 28 };
goblin.health += 10; // error: cannot assign to immutable field

foo: &mut T means you have a variable that refers to (&) a value and you are allowed to change (mut) the referred value (including fields, if it is a struct):

let val1 = &mut 2;
*val1 = 3; // OK

let val2 = &2;
*val2 = 3; // error: cannot assign to immutable borrowed content

Note that &mut only makes sense with a reference - foo: mut T is not valid syntax. You can also combine the two qualifiers (let mut a: &mut T), when it makes sense.