Robert's Rebellion, the war that put Robert and Cersei on the throne, was started because Robert was in love with Ned Stark's sister, Lyanna. He was under the belief that Rhaegar Targaryen, the heir to the throne at that time, had kidnapped Lyanna and was keeping her hostage. The reveal is such a big deal because it shows that Rhaegar was, in fact, in love with Lyanna, and she with him. They ran away together, the Grand Maester annulled Rhaegar's existing marriage to a Dornish princess (who is part of why the Red Viper had such a hard on for the Lannisters, since they killed her) and remarried him to Lyanna.
During the flashbacks with young Ned finding Lyanna in a bloody bed, it was revealed that she'd had complications from childbirth.
Taking these two events together, Jon is not a *******, but is a trueborn Targaryen/Stark child. Furthermore, being child of the former heir and male, he has a stronger claim to the throne than Danaerys.
