This word is to be used when no other word can be used to describe the cool factor, greatness, or overwhelming emotion of something. However, the something is neither sick, nor nasty. The combination of the words sick and nasty provide a higher connotation of coolness then even the words tight or wicked can provide. It is kind of ghetto.
Dude, your mom cooks some sick-nasty muffins.
That boy is wearing sick-nasty socks.