What does it mean?
Appreciative/sympathetic joy. Taking delight in one’s own goodness and that of others. One of the four “sublime abodes” (brahma-vihāra).
-from Access to Insight
Why does it matter?
If you read the Buddhist texts, you rarely hear the term “love”. The American teacher Gil Fronsdal points out that the reason is that Buddhist texts tend to be as specific as possible about interior states, and the “love” could mean so many things!
Muditā is an aspect of love. If you really, truly love someone, you are happy when they have successes. Do you know the feeling when your daughter plays really well at her piano recital? How she beams when everyone applauds? Do you feel her joy just as strong as you would if it had been your success? That is muditā.
Now have you had the experience when a close co-worker gets the promotion that you hoped might be yours? Do you give him a handshake and a smile but secretly burn with jealousy? What is the problem here? Lack of muditā.
Probably many of you are familiar with the practice of metta, loving kindness. Well, there is a very similar practice for muditā. How much happier you can be when you are truly happy at the joy of others! And how miserable is the alternative.