That green stuff inside a lobster is the lobster's liver and is called the tomally. The tomally is considered a delicacy to some people and disgusting to others. It should be noted that since the liver concentrates all the toxins taken into an organism, if the lobster came from polluted waters, the tomally should not be eaten.
In some lobsters there will also be pink stuff. This is the mature ovaries of the lobster. Again, some people relish this part of the shellfish, while others discard it.