If you're willing to do something, you're agreeable or ready. A willing participant in your play is someone who won't have to be coerced into taking part, but is happy to join you on stage.
Imagine that your neighbor asks whether you're willing to feed her cat while she's out of town. If you're open to helping her, perhaps even enthusiastic about spending time with a friendly cat, you're willing. Someone who's not willing would have to be persuaded or forced to do it. You can also use this adjective to mean "readily or enthusiastically done," as in the willing support you offer your best friend when she runs for class president.