Brief Summary
The Set-Up
Congress desperately needed a solution to the problem of slavery and statehood that adding Missouri posed, and this solution was found through the deft political maneuverings of a dude named Henry Clay. Missouri was established as a state with its own right of self-determination, and an invisible line was drawn through the U.S. defining where slavery could (and could not) be adopted.
The Text
The Compromise starts off with a sort of "statement of purpose," opening with the introduction of the Missouri as a state. It then goes through a section-by-section breakdown on the caveats to this introduction. First and foremost is a definition of just where exactly this "Missouri" place even is.
That might seems stupid and needlessly picky, but bear in mind that the single greatest asset America had in these early years was land. Land was used as an incentive and as a bargaining chip in all sorts of early American political and economic ventures, so determining exactly how much of it constituted Missouri was actually super-important.
The Compromise then goes on to breakdown the electoral makeup of the state and to declare that all free white male citizens twenty-one years or older will be able to vote and run for office. Provisions are made for the formation of a seat government (state capitol), as well as a state convention on the formation of a state constitution and other legislative minutiae.
The Compromise then makes further caveats on Missouri's statehood. It sets aside space and funds for schools, roads, and "seminary of learning" i.e. education beyond primary school. Water rights are set down, with provisions. Laws are set down for the parceling of land for military service. Protocol is set down for the acceptance of the state constitution by the Federal government. (Not going to lie: this part is a teensy bit dry.)
Finally, like a footnote, the most important part of the document is mentioned: that the U.S. would be split in two by law, between slave states and free states.
TL;DR
Missouri's a state, and the whole U.S. is now physically divided into slave and free states by law.