The tenth amendment is very simple in its formulation: it states that the federal goverment only has those powers that the constitution explicitely says, while state goverments has all powers except those that the constitution explicitely forbids.
In other words, the federal goverment only has explicit powers, while the states have both explicit powers and explicit powers.
The tenth amendment was written with the aim of preventing the federal government from becoming too powerful, because the founding fathers lived in an era where republicanism and federalism were rare (the United States was essentialy the only major republic in the world by thtat time) while tyrannies and absolute monarchies abounded. They were afraid that giving more power to the federal goverment would result in a new tyranny.
In Gitlow v. New York, 268 U.S. 652 (1925), the Supreme Court voted 7-2 to uphold the constitutionality of New York's Criminal Anarchy Statute of 1902, which prohibited advocating violent overthrow of the government.
