This is actually a fairly straight forward story from the Old Testament, though its factual details are debated. The situation is this:
Moses has been God's favorite and his brother Aaron and sister Miriam are getting jealous of that fact. They begin to gossip about Moses and the fact that he married a Cushite woman (that's not considered proper, as they are a different culture.) How this came about is debatable, because his wife Zipporah is not likely the Cushite woman in question. Some believe that it was a previous marriage, as Moses only had one wife.
However it happened, Aaron and Miriam are jealous that God is so "buddy buddy" with Moses and they begin to gossip about the fact that he married a Cushite. They question why God loves Moses so much to give him such a high place in his opinion. God hears this griping and is not pleased.
He calls all three out and lectures Aaron and Miriam, letting them know Moses is his number-one draft pick. He was angry at them for questioning His plan, and as punishment, he makes Miriam's skin start to rot off in disease. For whatever reason, he doesn't punish Aaron with an equally nasty consequence, though had God given him some disease it would have disqualified him from being high priest (though you'd think He could have at least sent some frogs or flies to plague him for a while!)
Resolution is straightforward. Aaron and Miriam say they are sorry to Moses and beg him to ask God to heal her, which he does. God has her sent into exile for a week before she comes back clean as a whistle and life goes on.
The main message seems to be twofold:
1) Don't gossip or speak badly about someone behind their back,
2) Guard your personal jealousies,
3) Don't mess with what God wants.