My only qualifications to explain this is I'm from Kansas and had to study this in history classes. Also, I brushed up using the wikipedia page http://en.wikipedia.org/wiki/Bleeding_Kansas

The Kansas-Nebraska Act of 1854 gave Kansans "popular sovereignty" which basically put up the issue of whether a state would be a "free-state" (no slaves) or a "slave-state" to a vote. If the vote was truly left to Kansans the vote was most likely going to end up creating a free-state, but pro-slavery men from Missouri and nearby would come in droves over to Kansas and vote in order to sway it in their favor.

Anti-slavery people mostly settled in lawrence and other nearby towns while pro-slavery forces settled further east and north in towns such as Atchison and Leavenworth creating a sort of border war between the forces (even though both these towns are in Kansas.) In that time period every vote really did count as there were only a total of 6000 votes (only 1500 "legit" Kansas registered voters) so conflict began to arose between the groups ending in "border ruffians" (pro-slavery missourians mostly) riding over to Lawrence and burning down the Free State hotel and doing some other damage.

By this time some anti-slavery Northerners including John Brown who supplied anti-slavery forces with guns hidden in Bibles otherwise known as Beecher's bibles. Although only 56 people died in the whole "war" the conflict climaxed during the Battle of Osawatomie where John Brown's forces engaged around 400 pro-slavery forces.

There was also conflict over which state constitution would become the real one with 4 total ones written and 2 supporting slavery and 2 against slavery. The Wyandotte Constitution supporting a free state was approved 1859 officially making Kansas a Free-state and swaying the control Anti-slavery supporters had over the direction of the United States.

The answers already here are great, but I just wanted to add some additional context. The slavery issue in the United States had always been a sort of a sore issue. From the founding of the United States up until the Civil War, slavery had been boiling quietly under everything -- but up until then it had been held in check by a series of compromises: the 3/5ths compromise and Missouri compromise are notable examples (the Missouri Compromise is a better example of this).

See, the thing was, the U.S. was becoming increasingly divided into two parts: the North and South. So much so that the South eventually decided that it would be alright to become it's own country. Because of this there was a constant political power play between the North and South. The North had a larger population because of urbanization and heavy industry, while the South maintained the sprawling "plantation" layout. Because of this, the House of Representatives, which is based on population, had the implied nature of legislating in favor of the North over the South, if it ever came down to that.

Thus, the only way the South could hope to keep the political playing field level was to balance out the Senate, where each State gets 2 senators regardless of population. And as the South became more and more defined by its "peculiar institution" and the North became more and more opposed to it, the admission of States became a major issue: the political balance of the Senate hinged on whether or not a state would be admitted as a Free or Slave state.

In the years leading up to the Civil War, each new state that was admitted would have to be balanced out for each side. Ideally, the South would gain one Slave State for each Free State that the North acquired, keeping the sway of the senators equal. However, because of politics listed above, it was rarely this simple. Because of the Kansas-Nebraska act, the North had the possibility of gaining two states and the South none.

In the end, the issue hinged on Kansas, and people on both sides would flood the state just to vote on it.

But by far the most fantastical thing to come out of all of this was a certain man named John Brown. A character that belongs in fiction and not of history, John Brown proclaimed himself as "God's chosen instrument" to tear down the abominable institution that was slavery. He made his entrance into United States politics during Bleeding Kansas, when he and a band of followers killed five men in front of their families, with broadswords. As stated above, John Brown was one of the leading figures of Bleeding Kansas, who would become a hero, and eventually a martyr, of folkloric proportions for the abolitionist cause.

In 1820, Congress passed the [Missouri Compromise] (http://en.wikipedia.org/wiki/Missouri_Compromise), which basically said that any territory in the once Louisiana Purchase north of the parallel 36°30' north was prohibited to have slavery. However, in 1854, the Missouri Compromise was repealed with the [Kansas-Nebraska Act] (http://en.wikipedia.org/wiki/Kansas%E2%80%93Nebraska_Act) which created the territories of Kansas and Nebraska for white settlement. The Missouri COmpromise was repealed because Kansas and Nebraska could rule on allowing slavery in the territory by rule of popular sovereignty (allowing the population decide the laws within the territory).

["Bleeding Kansas"] (http://en.wikipedia.org/wiki/Bleeding_Kansas) comes into the picture in 1854 when neighboring emigrants from Missouri came to secure Kansas for the expansion of slavery. Looking to secure "slave-statehood" and delegation in Congress, the slavery-endorsing Kansans fraudulently elected pro-slavery territorial leaders and wrote up laws favoring the expansion of slavery in 1855. Heads started to but in August when abolitionists gathered to formally reject the slave laws. In October, staunch abolitionist John Brown came to the Kansas territory to oppose the spread of slavery and influenced the immigration of more abolitionists. Violence commenced off and on until the break out the American Civil War in 1861.