The associative property says that you can calculate any two adjoining expressions, while the commutative property states that you can move the expressions as you please.
For instance, by associativity, you have (a + b) + c = a + (b + c), so instead of adding b to a and then c to the result, you can add c to b first, and only then add a to the result.
On the other hand, commutativity states that a + b + c = a + c + b, so instead of adding b to a and then c to the result, you can add c to a first and, lastly, a to all that. Note how associativity didn't allow this order. Read more