I’ve found that the hardest Buddhist concepts to understand are those which predate Buddhism in one way or another. One of these is the Buddha’s teaching on the four Brahma-viharas: metta, karuna, mudita, and upekkha.
In the Pali suttas they are almost always mentioned as a set without additional descriptions, such that it is hard to know where each begins and ends.
Thanissaro Bhikkhu’s article Head and Heart Together: Bringing Wisdom to the Brahma-viharas does a really great job of explaining the Brahma-viharas and their interrelationships in a way this hapless practitioner can understand:
Of these four emotions, goodwill (metta) is the most fundamental. It’s the wish for true happiness, a wish you can direct to yourself or to others. […] The next two emotions in the list are essentially applications of goodwill. Compassion (karuna) is what goodwill feels when it encounters suffering: It wants the suffering to stop. Empathetic joy (mudita) is what goodwill feels when it encounters happiness: It wants the happiness to continue. Equanimity (upekkha) is a different emotion, in that it acts as an aid to and a check on the other three. When you encounter suffering that you can’t stop no matter how hard you try, you need equanimity to avoid creating additional suffering and to channel your energies to areas where you can be of help.