Intercession is prayer or petition in favor of someone else. When you started wearing a cap of the rival baseball team, your baseball-mad family made an intercession to the gods to save your soul.
An intercession happens when you intercede in something, or act as a mediator or go-between to help solve a problem. Sometimes nations make intercessions in the internal affairs of other nations, if something brutal is happening. In that case, the intercession might involve sending troops, but often intercessions are verbal. If your friend is in trouble, you might make an intercession to try to get her out of trouble, especially if she's not good at explaining herself.