While it may also be a good vocabulary tool for an English class, the "Feelings Wheel" was actually developed as a therapy/counseling aid. I believe this one is a variant that does indeed focus on finding the right words for your emotions.

The categorization is intended to also help you understand your feelings after you identify them. If you have a general Sad feeling, you might drill down to figure out what specific flavor of sadness you might feel, for example maybe what you are really feeling is Ignored. Or the reverse — you might not immediately realize that a feeling of Inadequacy might be rooted in some Rejection and/or Fear on some deeper level.

There are also variants that are structured to help you identify the opposite of what you're feeling, so you can either identify a goal, a limitation, or maybe even a cause.

Here is an example of that variant, published by Dr. Gloria Wilcox in ~2001.

The Feelings Wheel is sometimes used in Emotionally Focused Therapy (EFT), a pretty successful type of couples counseling, the effectiveness of which is supported by some pretty decent research.

(It is also often cited by the less-reputable EFT, Emotional Freedom Techniques, which is a more "alternative", some might say wishy-washy, type of therapy. But their usage of the Feelings Wheel isn't necessarily bad.)