The point of something is the gist and principle of it. So, what's the gist of this vocab word? It's gist as well.
The reading is the same as the word 胸 (chest). So, the gist of your body is your chest (it's at the center, and holds everything together, right?). That's why these words are both read as むね.
I explained the gist of our family policy and how my husband and I don’t want to let our kid read comic books to the teacher.