For a summation of the plot without much spoiling, head over to Susan Arendt's recap, but if you're a fan of the books and want more in-depth, spoiler-rich discussion of what happens in "Baelor," read on, my friends!
In case that's not crystal clear, there are spoilers in here for both the rest of the TV show and the book series so please, tread carefully if you don't want to know the future events of either.
So, finally, Ned Stark gets killed. He is a man of honor, as we are told throughout the entire series by virtually every character including himself. But in the end, Ned chooses the life of his daughter, or so he thinks, by confessing to the trumped up charge that he conspired with Stannis and Renly Baratheon to take the Iron Throne from Joffrey. Stark fails so spectacularly, even at this, that it underlined something that Alex Macris said to me about A Song of Ice and Fire in the office one day in The Escapist offices. George R. R. Martin doesn't just kill characters off at a much higher rate than other fantasy authors, he makes sure to destroy the one thing that character cares about most before ending their life forever.
In the case of Eddard Stark, he prided himself on his honor. In the political machinations of the court of King's Landing, he was a wolf out of snow because he refused to do anything even remotely dishonorable. Through the visits of Varys the Spider to his cell beneath the Red Keep, we learn that Ned is perfectly fine with dying. His father and brother were killed by a King, and so was his sister Lyanna, so in some ways it is fitting for Ned to meet the same fate. He will die, but the Stark name will be remembered with honor still, and his children will uphold those same values.
But then Varys plants a seed in Eddard's thirst-addled mind. "What of your daughter? Is her life worth anything to you?" Poor Ned is manipulated even here in the dungeons, for Varys makes a big show about serving the realm and wanting peace but he is conspiring with the man from Pentos to put the Targaryens back on the Iron Throne. It's not clear what Varys' motivation is for wanting Ned Stark to confess and to convince his son Robb to bend the knee, but at this point no one should trust anything that comes out of Varys' mouth.
Unfortunately, Ned Stark did not learn that. When he is brought to the Sept of Baelor, he is ready to proclaim the lie of his crime so that Sansa will live and his family won't go to war. Stark will forfeit his honor, removing the trait that has defined his life, just so his House will survive. He believes he will live, but the Ned Stark that might have survived on the Wall would have been a shell of a man.