what does the Constitution guarantees to the people of every State the right to have slavery or not have it…each State being left free to decide for itself. mean
Tenth Amendment
http://en.wikipedia.org/wiki/Tenth_Amendment_to_the_United_States_Constitution
The statement you mentioned is a reference to a particular historical context in the United States. The phrase you quoted comes from the U.S. Constitution, Article IV, Section 2, commonly known as the "Fugitive Slave Clause." It was included in the original Constitution in 1787 and remained in effect until it was superseded by the 13th Amendment in 1865.
The clause states: "No person held to service or labor in one state, under the laws thereof, escaping into another, shall, in consequence of any law or regulation therein, be discharged from such service or labor, but shall be delivered up, on claim of the party to whom such service or labor may be due."
In simpler terms, this clause addressed the issue of runaway slaves and mandated that if a slave escaped to another state, they could be captured and returned to their owner, even if the state they escaped to had abolished slavery. It essentially guaranteed slaveholders the right to have their "property" returned to them.
The phrase "the right to have slavery or not have it…each State being left free to decide for itself," as you mentioned, refers to the broader concept of states' rights. It means that under the Constitution, each state had the freedom to determine whether or not to allow slavery within its own borders. It allowed states to establish their own laws and regulations regarding the institution of slavery.
It's important to note that this particular clause and the concept of states' rights played a significant role in the lead-up to the American Civil War and the debate over slavery in the United States. The language and interpretation of the Constitution have evolved over time, and many aspects of it, including the Fugitive Slave Clause, are viewed with historical context and in the context of subsequent amendments and legal developments.