Madame Web is a powerful cosmic being. She is the assistant to the Beyonder and teaches Spider-Man and the other Spider-Men important lessons.
When Spider-Carnage destroyed all of existence, the Beyonder stopped time and reversed it so that he and Madame Web could train six Spider-Men to combat the threat. Having finally began to date Mary Jane, Spider-Man tried to cut off his relationship with her, which she believed was preposterous. Despite this, she abided by his wishes and allowed him to go on without her, though warned him that the "two-headed dragon" would come for him. That two headed dragon was Green Goblin, having finally caused Norman Osborn to snap for the most part. Once he discovered Spider-Man's secret identity as Peter Parker, he held this over his head as Norman for the entire night during the gather he held and also attacked him in his Green Goblin identity.
He managed to get Mary Jane, and had her go into an alternate dimension. Spider-Man nearly left him for the same fate, but realized he could not, as it would go against his code of ethics. However, that did not stop Green Goblin from trying to attack him as he tried to help him. The plan had the reverse effect, and caused Green Goblin to fall into the alternate dimension. Following the failed attempt to save the love of his life, Spider-Man angrily requested her. She responded, and was told to stay away from him after he exclaimed his disgust in her riddles and her "supreme arrogance". She allowed him to be left alone, though promised she would be back when his real threat approached.
"Make a Wish"