What does incorporation mean as it relates to US government?

Incorporation means applying the US Constitution's Bill of Rights to the States to protect people's rights.

The Bill of Rights originally regulated only the actions of the federal government, and did not apply to the states. Each state had its own constitution, and all state constitutions included a bill of rights, many of which mirrored the language of the US Constitution, and some of which afforded greater freedoms.

In the 18th and 19th centuries, the Supreme Court often ruled in favor of state law when they were presented with cases that contradicted the first nine amendments (the 10th doesn't really confer any rights).

After the Civil War, the US government decided it needed a way to enable Reconstruction and supplement the Civil Rights Act of 1866, so Congress created the 14th Amendment, ratified by the States in July 1868. The Fourteenth Amendment was written in a way that could have forced the States to uphold the Bill of Rights of the US Constitution, but the Supreme Court decided not interpret it that way.

Congress passed the Civil Rights Act of 1875 to prevent businesses from discriminating against people, but the US Supreme Court declared the Act unconstitutional. They held the Fourteenth Amendment didn't give Congress authority to regulate private entities.

Some historians believe that the Fourteenth Amendment was meant to require States to follow the entire Bill of Rights (Total Incorporation), but others claim the individual Amendments were designed to be incorporated selectively. The Supreme Court has followed the doctrine of selective incorporation, upholding individual clauses within each Amendment only when they were relevant to cases before the Court and the justices thought the individual rights outweighed the states' rights.

As of 2010, some parts of the Bill of Rights remain unincorporated, such as the Third, Seventh, one clause of the Fifth, and part of the Eighth. The Second Amendment (right to bear arms) was not incorporated to the States until June 2010. Prior to the Supreme Court decision in McDonald v City of Chicago,(2010) States had the right to make their own regulations about owning and using guns.