'Ready' means that the time is right for you to do something. You are physically and mentally prepared.
'Willing' means that you are happy to do something if necessary. This is a synonym of 'prepared' in a different sense of the word - it means that you don't mind doing this. For example, you might say that a soldier is willing to die for a cause or for his country. Note that 'being willing' isn't the same as 'want' - if you are willing to do something means that you are not against this. An informal synonym is being 'OK' or 'cool' about it.
Often we use the two words together. If you say 'I'm ready and willing to help', it means that this is the right time, and that you are prepared physically, mentally and also emotionally.