Antebellum

Literally, antebellum means "pre-war." When studying American history, though, the decades leading up to the Civil War in particular are known as the "antebellum era" or "antebellum period." The antebellum period is generally considered to start after the War of 1812, and ends with the bellum—the Civil War. So, clearly, the Compromise of 1850 is included.

Territory

Yeah, yeah, we know that you know what territory is. The term is used a lot in the Compromise of 1850, but it's referencing something slightly more specific. In the 19th century, the U.S. was occupied with expanding the nation westward. Land that was taken over by the U.S. wasn't automatically made into new states. Until that land was populous enough to apply for statehood, it was known as a territory.

Mexican-American War (a.k.a. The Mexican War)

This war isn't really referenced in the Compromise of 1850, but it's very much in the background. You can read about the whole history here. The war led to the U.S. gaining a huge amount of land (most of the western U.S.), including California, Utah, and New Mexico: the states being discussed in the Compromise. The war also started as a dispute with Mexico over the border of Texas, a dispute that's finally settled in the Compromise.

Suffrage

Suffrage sounds bad, but it's actually really good. It's the right to vote. Black males got it in 1870. Women got it in 1920.

Legislative assembly

This is a broad term for the various types of legislatures that exist in the U.S., where representatives of districts are elected by the people living in that district.

Emoluments 

If a politician gets a monetary benefit from being in office (including their annual salary), that's an emolument. There's a clause in the Constitution preventing government officials from getting emoluments from foreign states, but the use of the word in the Compromise of 1850 doesn't deal with that. It's just about government salaries.

Apportion

To apportion means to divide and distribute. So you could, if you want to be fancy, create apportionments of pie for you and your family. Or just you; we won't judge.

Judiciary Act of 1789

The Compromise of 1850 references "the thirty-third section of the act of the twenty-fourth of September seventeen hundred and eightynine, entitled 'An Act to establish the Judicial courts of the United States.'" (Fugitive Slave Act.Section 1.1) The act created the Supreme Court of the U.S., while leaving the formation of lower courts to Congress. Section 33 legally establishes the "commit a crime, get arrested and tried in court" process that is pretty much the same today. Attorneys-General past and present can thank this Act for their jobs.