Javascript - can modify array passed to function only sometimes

The first function makes no attempt to modify the array. All it does is assign a new value to the parameter that, when it was called, was given a copy of a reference to the array. The variable a in the first function is just a variable with an object reference as its value. The assignment statement just changes its value, exactly as if your function had

    a = 5;

instead.

Note that you've declared the first function with a as a parameter - that symbol a hides the a outside the function.

The second function does modify the array because it calls a method on the array object that modifies it.

1. If a is passed into the function as a parameter, it is a local variable, so resetting its value will not affect the outside variable a.
2. But using methods that mutate array will change the outside variable like pop()/shift()/push/splice... and you can also use '.' to mutate the array directly like: arr.length=0;; push() can have multiple params, so you can: arr.push(...anotherArray).
3. If a is not passed as a parameter, but instead, the function reads it directly from the global scope, resetting value will directly change the variable. So, read it directly inside the function, and don't pass it as a parameter. Or pass it as a parameter, but using methods that will mutate the array to change its value.
4. See the examples: pass as a param

read from outside directly

Because in your first function, the statement a = initializes a new variable in local scope (it essentially translates to var a =) completely unrelated to the global a variable, whereas in the second function, you're calling upon and mutating the original array passed into it.

Try this

var a= [3, 4, 5];
function doesNothing() {
    a=[1,1,1];
}

function doesSomething() {
    a.push(6);
}

doesNothing(a);
console.log(a);    
doesSomething(a);
console.log(a);

Just inside doesNothing() the local variable a points to the same array as the the outer variable a. Then you assign a newly created array to the local a.

function doesNotNothing(a) {
  a[0] = 1;
  a[1] = 1;
  a[2] = 1;
}

This affects the contents of the array elements.