Adjectives modify nouns. Some sentences contain nouns so worthy of description that they require multiple adjectives. Now, everyone knows the rule that multiple adjectives are separated by commas when modifying the same noun. (Remember not to place a comma between the final adjective and the noun).
He ate the hard, chewy cheese.
Both "hard" and "chewy" are adjectives that modify the noun. Easy, right?
Not so fast. A comma is only needed between coordinate adjectives. This aspect of the rule is quite easy to break. Coordinate adjectives can be placed in reverse order or separated by the word "and". If you can do those two things without affecting the sense of what you are saying, then you have coordinate adjectives.
In the example above, we could have easily said:
He ate the hard and chewy cheese.
He ate the chewy, hard cheese.
Neither one robs the sentence of any meaning, so we have coordinate adjectives and they should be separated by a comma.
Non-coordinate adjectives, on the other hand, should not be separated by a comma. Non-coordinate adjectives are not equal. One takes precedence over the other.
An example using non-coordinate adjectives:
He drives a blue metal car.
Notice the absence of a comma? We would not say "a metal blue car" and we would not say "a blue and metal car", so we do not have coordinate adjectives.
As a rule of thumb, adjectives of size generally come first, followed by adjectives of age, color, then material.
When you're writing, it's easy to just start wedging commas between any two adjectives without thinking about whether they are really needed. We've all done it. Hopefully this little refresher will help us remember about coordinate versus non-coordinate adjectives.