“Secession” is a term that is most commonly used with reference to the time of the American Civil War. The war was caused in large part by secession. The South tried to secede from the North and the North did not want to allow this to happen.
Secession is something that is done by a state, a country, or other such entity. It happens when that entity withdraws from a group that it has previously agreed to be a part of. In the case of the American Civil War, the states had all agreed to be part of the United States. In 1860 and 1861, a number of states in the South decided that they no longer wanted to be part of the US. Therefore, they decided to withdraw, or to secede. This is what secession was. When the Southern states tried to secede, the war was all but inevitable.
In our times, Texas has talked about session and Quebec has talked about session.