Movie theater popcorn tastes much better than microwave popcorn. The difference between them is appreciable — that is, you notice it.
A good way to remember appreciable is to think of the related word appreciate. You appreciate the quality of the popcorn at the movie theater because it is significantly better than what you make at home. Of course, appreciable differences aren't always appreciated. There has been an appreciable improvement in the quality of televisions in the last 20 years, but if you've got an old TV, that isn't much comfort.