A little historical fleshing out:
First, one must recognize that "the admission of Kansas into the Union as a free state" was in fact a very, very big deal in 1855-56. At the time a territory, it was holding elections for a legislature to determine whether or not it would legalize slavery as a state. Kansas had an anti-slavery majority, but neighboring settlers from Missouri, pro-slavery, swarmed into Kansas by the thousands in order to stuff the ballots in favor of a pro-slavery legislature. The resulting legislature immediately legalized slavery, and the "free-staters" in Kansas just as quickly formed their own convention and drew up a plan for a free state. Keep in mind: this is 5 years before the Civil War broke out. The pro-slavery faction gathered a posse, marched to the town in which the free-staters had set up their headquarters, and sacked the entire town, burning the anti-slavery governor's house and destroying their printing presses. Out of this arose a series of conflicts on the borders of Kansas by armed bands of "Border Ruffians".
So, now you know why Mr. Sumner was so upset: both sides of the debate saw "Bleeding Kansas," as the conflicts were known, as signs of the other side bringing war into the Union. So, he gave his speech: in it, he focused especially on Senator Andrew P. Butler of South Carolina, who was just as militantly and loudly pro-slavery as Sumner was against it. Another quote, directed at Butler directly, claimed that Butler had "chosen a mistress... who, though ugly to others, is always lovely to him, though polluted in the sight of the world, is chaste in his sight... the harlot slavery." Though perhaps not too scandalous by our standards, such references in the 1856 United States Senate turned a few heads.
One such head was that of Mr. Brooks himself, a member of the House of Representatives, also from South Carolina.; the reason he was particularly enraged was that he was, in fact, Mr. Butlers's nephew.
Telcomac99, however, leaves out what might be the most dramatic and brutal part of the affair. According to Alan Brinkley: "Sumner, trapped in his chair (the Senate desks were bolted directly to the floor, as were the chairs, and thus one could not simply slide out of one's chair) rose in agony with such strength that he tore the desk from the bolts holding it to the floor. Then he collapsed, bleeding and unconscious."
Sumner was not able to return, in fact, for four years.
Source: Brinkley, Alan: The Unfinished Nation