The definition of a compromise is an agreement in which each side gives up something in order to get something in return. In the Missouri Compromise, what did each side give up and get?
In the Missouri Compromise, what each side had to give up was, in essence, having the whole country be their way.
Before the Missouri Compromise, the North would have preferred that no further land be opened to slavery. They particularly did not want Missouri to become a slave state as it was north of the Ohio River, which they saw as the border for slavery. This idea can be seen, for example, in the Tallmadge Amendment, which proposed that all slaves in Missouri be freed when they reached age 25.
While this was not as important to the South, it would have preferred that slavery be legal in all of the new territories. It did not want slavery to be limited to the South for fear that the South would eventually be overwhelmed in both the House of Representatives and the Senate.
So, both sides gave something up and got something. The South got Missouri to enter the Union as a slave state. The North got slavery prohibited in the rest of the Louisiana Purchase north of the 36°30’ line.